In contention-based satellite communication system, collisions between data packets may occur due to the randomly sending of the packets. A proper delay before each transmission can reduce the data collision rate. As classical random multiple access protocol, the slotted ALOHA(S-ALOHA) reduces the data collision rate through time slot allocation and synchronous measures. In order to improve the stability and throughput of satellite network, a backoff algorithm based on S-ALOHA will be effective. A new adaptive backoff algorithm based on S-ALOHA using grey system was proposed, which calculates the backoff time adaptively according to the network condition. And the network condition is estimated by each user terminal according to the prediction of the channel access success ratio using the model GM(1,1) in grey system. The proposed algorithm is compared to other known schemes such as the binary exponential backoff(BEB) and the multiple increase multiple decrease(MIMD) backoff. The performance of the proposed algorithm is simulated and analyzed. It is shown that throughput of the system based on the proposed algorithm is better than of system based on BEB and MIMD backoff. And there are also some improvements of the delay performance compared to using BEB. The proposed algorithm is especially effective for large number of user terminals in the satellite networks. A proper delay before each transmission can reduce the data collision rate. As classical random multiple access protocol, the slotted ALOHA (S-ALOHA ) reduces the data collision rate through time slot allocation and synchronous measures. A new adaptive backoff algorithm based on S-ALOHA using gray system was proposed, which calculates the backoff time adaptively according to the network condition. And the network condition is estimated by each user terminal according to the prediction of the channel access success ratio using the model GM (1,1) in gray system. proposed algorithm is compared to other known schemes such as the binary exponential backoff (BEB) and the multiple increase multiple decrease (MIMD) backoff. The perfor mance of the proposed algorithm is simulated and analyzed. It is shown that throughput of the system based on the proposed algorithm is better than of system based on BEB and MIMD backoff. And there are also some improvements of the delay performance compared to using BEB. The proposed algorithm is especially effective for large number of user terminals in the satellite networks.