EOS (Earth Observing Satellite) imaging scheduling process should generate the sequence of imaging requests. It is a complex combinatorial optimization problem. Considering the imaging constraints of EOS, to make replete use of the resource, the label vertex digraph without circuit as the model of imaging scheduling problem was adopted. On the basis of this model, a multi-objective scheduling method, based on the Strength Pareto Evolutionary Algorithm 2, was presented and also genetic operators to handle the imaging constraints were proposed. This method was tested on three real problems with two objective functions. From the results, it can be said that the proposed method can resolve the EOS scheduling problem efficiently.