This paper presents a multi-objective satellite scheduling problem for very large areal observation in response to various requests. The objectives are to maximize the total profits of generated observation schedule and the high efficiency of the satellite utilization simultaneously. To address the satellite scheduling problem, we first demonstrate a detailed problem description and then transform the problem into set covering problem within several criteria and constraints. Based on that, a mathematical model is established. To solve the problem, a new three-phase solving framework is proposed. In the discretizing phase, an area discretization method is adopted to establish the evaluation system. In the target decomposing phase, area target is decomposed into strips and corresponding visible time windows are calculated. In the scheduling phase, a multi-objective genetic algorithm is introduced to generate an optimal observation schedule taking account of the distinct aspect of objectives. Through extensive computational experiments on realistically generated problems in various scenarios including real-world data from China’s satellite platform, the effectiveness and reliability of the proposed solving framework are verified.