To solve the problems such as the unfairness existing when standard TCP connects with different RTT competing bandwidth, the window over-fast growth caused in the late phase of slow start and etc., a new TCP slow start algorithm for improving, termed SS+, is proposed. In the early slow start phase, using SS+ can keep the congestion window exponential grow; in the late phase, the window control growth factor in direct proportion to RTT is introduced to increase the congestion window of TCP connecting with larger RTT faster, otherwise the increase will be slower. Performance analysis and simulation results show that by using SS+ algorithm the congestion window growth rate is slowed down and the TCP connection with smaller RTT in the aggressive bandwidth competition is weakened in the late slow start phase. To a certain extent, by using SS+ algorithm a fair sharing of available bandwidth between TCP connections with different RTT is obtained. And SS+ algorithm is easy to realize and only requires the TCP source revised. This SS+ algorithm has some theoretical and practical application value.