To study nonlinear characteristics of freak wave, this research focuses on the spatial evolution process of weakly high-order nonlinear waves propagating over a sloping bottom. We use modified Non-Linear Schrö dinger (NLS) equation considering bathymetry change to conduct a Monte-Carlo simulation, and it gives spatial evolution of kurtosis and skewness of wave surface elevation at different cases. The effect of water depth and initial quasi-resonant interactions on wave evolution have been explored. We also discuss the relationship between kurtosis, skewness and maximum wave height, as well as their performance around critical water depth for four wave resonant interactions. The results indicate that in deep water initial BFI significantly effects kurtosis and occurrence probability of freak wave. From deep to shallow water, transition region around critical water depth makes this effect become complicated.