When the base station knows imperfect channel state information (CSI) with limited estimation errors, the robust precoding scheme based on signal to interference plus noise ratio (SINR) constraints is less feasible. In this paper, a precoding scheme based on signal to leakage plus noise ratio (SLNR) is proposed for MIMO downlinks. By solving a series of semidefinite program (SDP) problems, the proposed design minimizes the total transmitted power under each user's SLNR constraint. At the same time, it can dynamically allocate each user's SLNR threshold according to their channel states, so it is more feasible than the similar SINR-based precoding scheme. In the case of having higher estimation errors for CSI, a channel modification matrix based on the minimum mean square error (MMSE) is used to increase feasibility of the proposed precoding method. Simulation results show that the proposed precoding scheme is robust to channel estimation errors, and can achieve optimal solutions with higher probability. Moreover, it has a better bit error rate performance than similar SINR-based precoding.