Because of the option grants and other long-term incentives, CEO contracts feature increasing pay-performance sensitivity (PPS). Previous literature use different theories to explain the convexity in CEO pay structure, but the optimal non-linear contract exhibits convexity only around the central region. In this paper, I make three contributions: First, I show that when CEOs assign higher probability to extreme cases, the optimal non-linear contract features convexity even if performance goes to the far end. This explains the existence of incentive pay and increasing PPS in CEO contracts. Second, I find that when stock returns follow a normal distribution, probability weighting generates an asymptotically normal distribution with different parameters. I use this sigma-mu transformation to approximate the probability weighting process, which helps give the close-form solution for the optimal non-linear CEO contract. Finally, I calibrate the model with observed contracts of US CEOs and show that the model with probability weighting works better than the model without probability weighting for a wide range of parameters. To summarize, shareholders exploit probability-weighting to provide cheap incentives that encourage CEOs to exert more effort.