Satellite weekly task scheduling is an important procedure for the Satellite Run and Management System, and it exerts influence on the effectiveness of satellite system. Different from the function and the characteristics of daily task scheduling, weekly task scheduling includes not only the technology problem but also the management problem. This study mainly expounds three aspects of work: firstly, analyzing the demand and the characteristic of weekly task scheduling, explaining four main functions of weekly scheduling, and constructing a hierarchical scheduling framework; secondly, summarizing optimization objects and constraint conditions, and building the weekly task scheduling model with considering the task overloading factor; thirdly, combing the Gene Algorithm and the Simulated Annealing Search to solve the model, while instigating the heuristic rules and introducing distributed parallel computing strategy.