Inverter nonlinearity and nonsinusoidal back electromagnetic forces (EMFs) can cause large current harmonics in permanent magnet synchronous machine (PMSM) drives, especially for those with low inductance, resulting in increased torque ripples and losses. With deadbeat predictive current control (DBPCC), the feature of high control bandwidth can reduce, to some extent, the unwanted low-order current harmonics but not remarkably. Therefore, this article presents a novel method, named adaptive harmonic reference correcting current injection, to compensate the effects of inverter nonlinearity and back EMF harmonics for DBPCC of PMSM drives. It can effectively eliminate all the resultant current harmonics caused by nonideal factors and maintain the high dynamic responses of DBPCC, even under the conditions where the sampling-to-harmonic frequency ratios are quite low. Furthermore, the proposed method requires no information about both the machine and inverter. It can be easily implemented and is parameter insensitive. Extensive simulation and experimental results of a prototype low-inductance PMSM drive have been presented to verify the proposed method.