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Rate-splitting multiple access (RSMA) is a key enabling technology for beyond 5G networks due to its robustness against imperfect channel knowledge. In this paper, we consider both the imperfect channel state information (CSI) at the receiver (CSIR) and imperfect CSI at the transmitter (CSIT) and propose a max-min fairness optimization framework relying on RSMA to guarantee each user's minimum level of quality of service (QoS). First, we formulate the max-min fairness optimization problem that has non-convexity. To transform the non-convex problem into a convex problem, we apply the semi-definite relaxation (SDR) and convex-concave procedure (CCP) to the proposed algorithm. From simulation results, we confirm that RSMA is still a robust scheme over conventional multiple access schemes for both imperfect CSIT and CSIR.