This paper derives the stochastic process of Delta hedge gain under the general jump diffusion process. Theoretically, Delta hedge gain contains four components, including jump risk and risk premium of jump risk in our assumption. The theoretical result is tested with SPX option data. The empirical result indicates that complex roles jump affects option prices. The result is significant when the model risk and market efficiency effects are controlled. It is found that in different financial environments, different types of options are affected differently by the jumps.