In order to solve the security threats that dependent tasks scheduling problems face under the heterogeneous grid environment, this paper takes into account the inherent safety and behavior of security of the grid resource node and the reliability of measurement functions in the grid resource node. In addition, the behavior in credibility assessment strategies are also constructed. In order to establish the subordinate relationship between the security requirements of the task nodes and resources security attributes, security benefits of the membership functions are defined. Hence, a grid task scheduling model for security integration is established. On this basis, the requirement representation model and the grid resource topology model are defined; thus, the models of doubleobjective optimization of grid task scheduling are proposed. In order to solve this model, the definition of depth values and the sort of coupling is introduced when dealing with the constraints between tasks. A particle evolution equation is re-defined and re-designed to consider the specific characteristics of the grid task scheduling problem. At the same time, a selection strategy is defined, based on the uniformly distributed vector and concentration of particles. Thus, this paper presents a multi-objective optimization of grid task scheduling particle algorithm, and the algorithm is proved to be viable by applying the relevant knowledge of a probability theory. Simulation results show that compared with similar algorithms, under the same conditions, this algorithm has a faster convergence speed and a better performance in double-objective optimization.