Multi-User scheduling is a challenging problem under the relaying scenarios. Traditional schemes, which are based on the instantaneous signal-to-interference-plus-noises ratios (SINRs), cannot solve the inherent disparities of the qualities between different links. Hence, the system performance is always limited by the weaker links. In this paper, from the whole system throughput view, we propose an optimal multi-user scheduling scheme for the multi-user full-duplex (FD) buffer aided relay systems. We first formulate the throughput maximization problem. Then, according to the characteristics of the Karush-Kuhn-Tucker conditions, we obtain the optimal decision functions and the optimal weighted factors of different links of the proposed scheme. Simulation results show that the proposed scheme not only solves the disparities of the qualities between $S_i$-$R$ and $R$-$D_i$ links, but also that between different $S_{i}$-$R$ or $D_{i}$-$R$ links, which can be used as guidance in the design of the practical systems.