Recently, model-based predictive current control (MB-PCC) has been presented as a good alternative to classical control algorithms in terms of simplicity and performance reliability. However, MB-PCC suffers from the high dependence on system parameters, which may deteriorate its performance under parameters variations. On the other hand, Synchronous Reluctance Motors (SynRMs) are susceptible to suffer from inductances variations due to the magnetic saturation. Accordingly, in this paper a new model-free predictive current control of SynRMs based on a recurrent neural network (RNN-PCC) is developed and proposed. The proposed RNN-PCC relies on the identification of the SynRM currents without considering any parameters. Simulation and experimental results show that both RNN-PCC and MB-PCC have similarly excellent dynamics, while better control performance and tracking errors can be achieved thanks to the proposed RNN-PCC.