The scheduling of Earth Observation Satellite (EOS) data transmission is a complex combinatorial optimization problem. With the development of remote sensing applications, a new special requirement named data transmission oriented to topics has appeared. It supposes that the data obtained from each observation activity by satellites belong to certain observation data topics, and every observation data topic has completeness and timeliness requirements. Unless all of the observation data belonging to one topic has been transmitted to the ground before the expected time, the value of the observation data will be decayed sharply and only a part of the rewards (or even no reward) for the data transmission will be obtained. Current researches do not meet the new data topic transmission requirements well. Based on the characteristics of the problem, a mathematic scheduling model is established, and a novel hybrid scheduling algorithm based on evolutionary computation is proposed. In order to further enhance the performance and speed up the convergence process of our algorithm, a domain-knowledge-based mutation operator is designed. Quantitative experimental results show that the proposed algorithm is more effective to solve the satellite observation data topic transmission scheduling problem than that of the state-of-the-art approaches.