The microlens array (MLA) is used in the flexible pupil shaping module of lithography illumination system for energy balance. However, the coherence of the light source can lead to interference patterns. Most of the decoherence methods are restricted for the pulse laser and the scanning exposure application. To solve this issue, a specific random phase plate (RPP) is designed to eliminate the interference patterns caused by the coherence of the light source. The model of partially coherent light propagation in the MLAs homogeneous system is established based on the mutual intensity theory, and the genetic algorithm is introduced to design a high-performance RPP. The corresponding measurement device is constructed, and the intensity of the image plane light field is measured. Experiment results indicate that the intensity integral non-uniformity is 32.14% in the x-direction and 66.04% in the y-direction without the RPP, and the intensity integral non-uniformity is 22.95% in the x-direction and 19.18% in the y-direction with the RPP, which verifies the feasibility of the proposed method.