David, a young boy, lives with his father when his mother left them when he was 5. While playing on ice, he falls through it. He instinctively teleports ('jump') to the local library. He grows older and his drunkard dad threatens him. He 'jumps' to the library again, because that's where he feels the safest.
As a young man, he practices his skills more and more until he could control exactly how he 'jumps'. He visits a local bank and sees the vault. That night, in his motel room, he 'jumps' back and forth from the bank to his hotel room, stealing a lot of cash and gold bars. Later on, he stays in New York in a fancy condominium where he keeps pictures of 'jump sites' (where he can go by 'jumping') and a vault for all his cash and loot.
One night, he comes home to find Roland Cox, a Paladin, in his apartment. The Paladins are a secret society devoted to hunting down Jumpers, who they consider as abominations. Roland uses plenty of high-tech weaponry to try and stop David from 'jumping' such as an electrocuted wire because 'electricity through the brain of a jumper prevents him from 'jumping''. However, David manages to escape by locking himself up in his vault and 'jumping' away.
David then visits a local bar and finds his childhood crush Millie working as a bartender. He also encounters Mark, his childhood bully. As Mark makes lewd comments toward Millie, David fights him. David pushes Mark through a back gate and they both disappear; David 'jumps' them both in a bank vault. There, Mark is left. David then offers to bring Millie to Rome (her childhood dream was to visit the city) while Mark is interrogated by Roland.
In Rome, David impresses Millie with his wealth which he claims 'came from working in banking'. He brings Millie to a tour of the Colosseum. David 'jumps' around the place unlocking unauthorized zones for Millie. While touring, he spots Griffin, an English Jumper. Griffin has been tracking down David. The 2 are attacked by Paladins, but they manage to outwit and kill all of them. David follows Griffin to his lair in the desert through Griffin's 'jump scar', a fragmentary portal that exists for a short period of time after a Jumper's successful 'jump'. In his lair, Griffin narrates of an old blood feud between the Paladins and the Jumpers, and how he is trying to track down as many Paladins as he can and kill as many as he can. Griffin is also skillful enough in his 'jumping' that after stealing a Mercedes SLR, he 'jumps' the car through traffic recklessly.
Returning to Rome, David seeks to send Millie back home. David is then arrested by the Polizia for trespassing and while in custody, he is visited by a lawyer who turns out to be his mother. David is warned by his mother that the Paladins are about to come for him. After Millie gets on the plane, David 'jumps' back to his childhood home to check on him. While in Rome, Roland arrives at David's home and sends subtle threats to David's father William. William refuses to sell out David and is killed by Roland. David arrives at the scene too late and 'jumps' his father to a local hospital. David then jumps into Griffin's lair and prepare an attack on the Paladins. However, the Paladins have a new technology that allows them to find 'jump scars' and go through them, and with this, they find Griffin's lair. In the attack, Griffin attacks them with a flamethrower while David gets trapped on a wall with electrocuted nets. Outside, Griffin 'jumps' back to London, holds a double-decker bus, and 'jumps' back in his lair, attempting to crash it on Roland. Roland manages to escape through the 'jump scar', taking Millie with him.
Griffin readies a bomb to kill Roland and the Paladins, but David refuses to let him, saying that it will kill Millie too. David steals the detonator and the two fight and chase each other around the world through each others' 'jump scars'. David finally traps Griffin in an electrified power pylon, preventing Griffin from 'jumping'. David jumps to Millie's apartment where she is trapped by Roland. David is captured, but he concentrates his entire being into 'jumping' Millie's entire apartment in a lake. The Paladins' equipment are destroyed, and David jumps Millie and Roland back into the library. He then jumps Roland into a cave, saying that 'he's different and could have 'jumped' Roland in the ocean with sharks, but he didn't'. Instead, the camera zooms out and we see Roland stuck in a cave in the middle of the Grand Canyon.
David visits his mother and learns that she is, in fact, a Paladin. She tells him she left because as a Paladin, she was supposed to kill David, her own son. She tells him that he should leave, and because she loves him, will give him a head start. David leaves and meets up with Millie, and the scene closes with them 'jumping' somewhere.