The mission of Earth observing satellite (EOS) is to acquire photographs of specified areas on Earth surface at the requests of users. The goal is to select a feasible task sequence to maximize the sum of weights. This research presents the mission planning problem of the next-generation agile Earth-observing satellite(AEOS). The complex user requests(including multi-strip area, real time download request, and stereoscopic request) and complex satellite constraints were considered, covering eight satellite actions(including observe action, data download, SSR Erase action, attitude movement, heliocentric pointing, geocentric pointing, and instrument action). A chronological look ahead algorithm was designed to solve the problem, heuristic rules based on expert knowledge were used to make choices and arrange satellite actions, which satisfy all satellite physical constraints and operational constraints. For the current experiment instances and applications, the algorithm can give results in very short time. Experiment results suggest that our algorithm works well for the agile earth-observing satellite planning problem.