Fog computing provides users with data storage, computing, and other services by using fog layer devices close to edge devices. Tasks and resource scheduling in fog computing has become a research hotspot. For the multi-objective task-scheduling problem in fog computing, an adaptive multi-objective optimization task scheduling method for fog computing (FOG-AMOSM) is proposed in this paper. In this method, the total execution time and the task resource cost in the fog network are taken as the optimization target of resource allocation, and a multi-objective task scheduling model is designed. Since the objective model is a Pareto optimal solution problem, the global optimal solution can be obtained by using multi-objective optimization theory and the improved multi-objective evolutionary heuristic algorithm. Moreover, to obtain a better distribution of the current task scheduling group, the neighborhood is adaptively changed according to the current situation of the task scheduling group in fog computing, which avoids the problem that the neighborhood value caused by the neighborhood policy in the multi-objective algorithm affects the distribution of the task scheduling population. This algorithm is used to solve the non-inferior solution set of the utility function index of fog computing task scheduling to try to solve the multi-objective cooperative optimization problem in fog computing task scheduling. The results show that the proposed method has better performance than other methods in terms of total task execution time, resource cost and load dimensions.