Satellite transmission scheduling problem (STSP) is an important part of satellite mission planning and one of the bottlenecks in satellite development. This paper established a mathematical model for the STSP problem. After that, we proposed an effective heuristic scheduling algorithm (HSA) and task scheduling algorithm (TSA) based on the characteristics of the problem. In addition, in the TSA, a greedy task scheduling method is adopted to ensure that the task arrangement is more compact in order to obtain a better solution. We verified the effectiveness of HSA and TSA algorithms under different task scales and proved that this algorithm can solve the STSP problem well. HSA and TSA all have good performance in terms of total revenue, number of tasks completed, and time utilization.