Rate-splitting multiple access (RSMA) has appeared as a powerful transmission and multiple access strategy for multi-user multi-antenna communications. Uniquely, this paper studies the optimization of the sum-rate of RSMA with imperfect channel state information (CSI) at the transmitter (CSIT) and the receivers (CSIR). The robustness of the RSMA approach against imperfect CSIT has been investigated in the previous studies while there has been no consideration for the effects of imperfect CSIR. This motivates us to develop a robust design relying on RSMA in the presence of both imperfect CSIT and CSIR. Since the optimization problem for the design of RSMA precoder and power allocations to maximize the sum-rate is non-convex, it is hard to solve directly. To tackle the non-convexity, we propose a novel alternating optimization algorithm based on semidefinite relaxation (SDR) and concave-convex procedure (CCCP) techniques. By comparing simulation results with conventional methods, it turns out that RSMA is quite robust to imperfect CSIR and CSIT, thereby improving the sum-rate performance.