Metasurfaces offer an unprecedented opportunity for flexible manipulation of electromagnetic wave. The azimuth-rotation-independent (ARI) polarization conversion metasurface (PCM) is an ultrathin device, which could convert an arbitrary linearly-polarized incident wave to its cross-polarized state. However, the bandwidth of an ARI PCM with a high cross-polarized transmission is usually limited. Here, a topology optimization method of multi-feature points based on the differential evolution (DE) algorithm is adopted to enhance the bandwidth of the traditional ARI PCM while maintaining a high transmission and polarization conversion ratio. The simulated results of the optimized structure indicate a 2.08 times bandwidth expansion in the cross-polarization conversion compared with the original structure. In addition, the measured results are consistent with the simulated ones and the ARI characteristic is validated. The proposed method provides a promising route for efficient high-performance metasurface designs.