For the grinding marks phenomenon formed in cross grinding of plane, spherical and aspheric optical elements would reduce the surface quality, surface strength and optical performance of workpiece, which would increase subsequent polishing time and wastage of polishing resources, the suppression strategies of grinding marks based on adjusting grinding traces distribution simulation was investigated. According to the distribution equations of grinding traces and the scallop height, the possibility of two grinding marks suppression strategies was discussed, one of strategy was based on matching grinding parameters and the other one was on grinding traces superposition without depth of cut. Based on the two strategies, the grinding verification experiments were carried out. The results showed that the grinding marks were suppressed by the matching parameters strategy, which cracks and deep grinding traces were less, surface roughness and its homogeneity were better, surface waviness was smaller when ground by matching parameters with the phase shift of 0.618. Besides, when grinding traces superposition strategies were used to process experiments, the morphology and surface roughness did not change much, but all homogeneity of surface roughness were fine with the increasing of superposition times. Moreover, the surface waviness significantly decreased from 90 to 30 nm after 3 superposition times, the grinding marks were also suppressed by the grinding traces superposition without depth of cut. This research would provide references and ideas for grinding aspherical surface with high surface quality and efficiency, and low energy.