This paper studies scheduling activities with stochastic duration of activities, and constructs a multi-objective optimization model, aiming at the balance between makespan and resource leveling. In this paper, a multi-objective optimization genetic algorithm based on fast non-dominated sorting (NSGA-II), is selected for solving the problem. In order to satisfy precedence constraints, an encoding scheme based on logical relationships, a crossover operator where sets are crossover units and mutation which is performed within the set are designed. Finally, the effectiveness of the proposed NSGA-II algorithm is illustrated by comparing the mutual coverage of the solution set of the improved with the original. The mutual coverage solution of sets refers to the mutual dominance between the Pareto optimal solutions produced by different algorithms.