The satellite cannot simultaneously serve all users due to the large number of users on the earth. User grouping algorithm, which different users are divided into several groups to be served consecutively by the satellite in different time slots, is studied to cluster all customers. In this work, two greedy user grouping algorithms are proposed. Adaptive user grouping for sum-rate maximization (AUG-SM) algorithm with variable number of groups can schedule all users to guarantee the fairness between the users. Aiming at maximization sum-rate of satellite communications, certain user grouping for sum-rate maximization (CUG-SM) algorithm with certain number of groups is proposed. Simulation results show that the proposed algorithms achieve favorable sum-rate performance.