This paper presents a finite control set model predictive control (FCS-MPC) strategy for the AC/DC matrix converter used in grid-connected battery energy storage system (BESS). First, to control the grid current properly, the DC current is also included in the cost function because of input and output direct coupling. The DC current reference is generated based on the dynamic relationship of the two currents, so the grid current gains improved transient state performance. Furthermore, the steady state error is reduced by adding a closed-loop. Second, a Luenberger observer is adopted to detect the AC input voltage instead of sensors, so the cost is reduced and the reliability can be enhanced. Third, a switching state pre-selection method that only needs to evaluate half of the active switching states is presented, with the advantages of shorter calculation time, no high dv/dt at the DC terminal, and less switching loss. The robustness under grid voltage distortion and parameter sensibility are discussed as well. Simulation and experimental results confirm the good performance of the proposed scheme for battery charging and discharging control.