In order to reduce the risk of thinning and cracking during stamping for zirconium alloy strips, for the strip progressive stamping, its feature forming has the same stamping speed, blank holder force and friction coefficient, a simplified finite element model of strip was established, and the accuracy of finite element simulation was verified by physical test. Then, support vector machine was used to establish thinning rate prediction models for strip spring and rigid convexity feature respectively, and aiming at the multi-objective problem of overall strip thinning during forming process, based on non-dominated sorting genetic algorithm and entropy weight TOPSIS method, the Pareto front solutions and the comprehensive ordering of corresponding process parameters under three lubrication conditions were calculated. The results show that the thinning rate of rigid convex feature for strip is more sensitive to the change of process parameters than that of spring feature, and the optimum stamping process of strip varies obviously under different lubrication conditions. Thus, under the common no-lubrication condition, when the stamping speed is 134.41 mm·s-1 and the blank holder force is 7862 N, the strip progressive stamping has the minimum risk of thinning and cracking.