This study aims at eliminating unwanted harmonics in current control of a five-phase non-sinusoidal permanent magnet synchronous machine (PMSM) in an open-end winding configuration. The machine is supplied by two voltage source inverters (VSIs) using a single DC-bus voltage. High-frequency harmonics, caused by the zero-sequence current with the inverter switching frequency, have been significantly reduced by using a proper pulse width modulation (PWM) strategy. Meanwhile, low-frequency current harmonics are generated by unwanted harmonics of the back electromotive force (back-EMF) and by the inverter nonlinearity. In this study, the low-frequency current harmonics are nullified by simple adaptive linear neural networks (ADALINEs) in rotor reference frames combined with the back-EMF compensation. As a result, the quality of current control is improved. The effectiveness of the proposed strategies is verified by numerical results