Conventional constellations, in high orbit, are usually designed for the global coverage, and cannot obtain the information of important area when they are in emergency conditions. To solve the problem, a design method of operationally responsive small satellite constellation was proposed, which can satisfy the wide range of needs. A corresponding mathematical model was built in the paper. Firstly, the geometry analytic methods were applied to study the influence of the location relationships of track of subsatellite point and the coverage circle on coverage and responsive ability of specific target area, and the orbit which can satisfy the needs was designed. Then, based on the orbit, a small satellite constellation design scheme was proposed. Finally, taking the city YA＇an as the target area, simulations with STK software and Matlab software were carried out to demonstrate that the simulation result is the same as that of mathematical model, the constellation scheme can bring about 126s coverage for every 1150s. And it verified the correctness of the model.