An accurate definition of a system model significantly affects the performance of model-based control strategies, for example, model predictive control (MPC). In this paper, a model-free predictive control strategy is presented to mitigate all ramifications of the model's uncertainties and parameter mismatch between the plant and controller for the control of power electronic converters in applications such as microgrids. A specific recurrent neural network structure called state-space neural network (ssNN) is proposed as a model-free current predictive control for a three-phase power converter. In this approach, NN weights are updated through particle swarm optimization (PSO) for faster convergence. After the training process, the proposed ssNN-PSO combined with the predictive controller using a performance criterion overcomes parameter variations in the physical system. A comparison has been carried out between the conventional MPC and the proposed model-free predictive control in different scenarios. The simulation results of the proposed control scheme exhibit more robustness compared to the conventional finite-control-set MPC.