The main purpose of this study was to research and develop maximum power point tracking (MPPT) of a photovoltaic module array (PVMA) with partial module shading and sudden changes in solar irradiance. Modified cat swarm optimization (MCSO) was adopted to track the global maximum power point (GMPP) of the PVMA. Upon a sudden changes in solar irradiance or when certain modules in the PVMA were shaded, the maximum power point (MPP) of the PVMA will change accordingly, and multiple peak values may appear on the power–voltage (P-V) characteristic curve. Therefore, if the tracking pace is constant, the time required to track the MPP might extend, and under certain circumstances, the GMPP might not be tracked, as only the local maximum power point (LMPP) can be tracked. To prevent this problem, a maximum power point tracker based on MCSO is proposed in this paper in order to adjust the tracking pace along with the slope of the P-V characteristic curve and the inertia weight of the iteration formula. The initial voltage for tracking commencement was set to 0.8 times the voltage at the maximum power point of the PVMA under standard test conditions. Firstly, MATLAB 2022a was used to construct the four-series, three-parallel PVMA model under zero shading and partial shading. The feedback of PVMA voltage and current was obtained, where the GMPP was tracked with MCSO. From the simulation results, it was proven that, under different shading percentages and sudden changes in solar irradiance for partial modules in the PVMA, the MCSO proposed in this paper provided better tracking speed, dynamic response, and steady performance compared to the conventional CSO.