For slope instability caused by rainfall, there are some differences between ideal rainfall conditions and actual rainfall conditions. In order to study the stability of slopes under heavy rainfall, this paper therefore takes the “7.20” special rainstorm in Zhengzhou as an example. Four factors, namely average annual rainfall q, soil permeability coefficient anisotropy kr, water table height hw, and suction friction angle φb, were selected as variables. The finite element method was used to analyze the variation rule of initial pore water pressure (IPWP) at the top and bottom of the slope under various factors during the rainfall process, the limit equilibrium method was used to calculate the safety factor (Fs) after the rainfall, and the grey correlation analysis method was used to analyze the sensitivity of factors affecting slope stability under heavy rainfall. The result shows that the pore water pressure at the top of the slope varies more than that at the bottom of the slope during rainfall. The lower the initial pore water pressure, the lower the safety factor of the slope at the end of rainfall. The sensitivity of each factor to the slope safety factor is in the following order: φb>kr>hw>IPWP.