In modern power system, the renewable energy generation has been widely used, putting forward higher requirements for multi-port bidirectional converters. Series resonant multi-active-bridge (SR-MAB) converter, which has the advantages of bidirectional power flowing capability, electrical isolation and DC bias suppression, is studied in this paper. The operation principle and power flow are analyzed. However, the traditional model predictive control relies on the precise model heavily. The active power of SR-MAB converter is relative to multiple control variables, which makes it difficult to obtain the optimal solution in the next control cycle. Therefore, a model-free predictive control method is proposed to realize the fast dynamic response. The control target deviation is classified on the basis of the load type firstly. Then, the data-driven model with Kalman filter is established to achieve zero control target deviation. Finally, the simulation results verify the ability of the proposed control scheme in (i) achieving fast dynamic response, (ii) reducing the coupling among ports, (iii) accurately tracking the control targets.