Deadbeat Predictive Current Control (DPCC) has emerged as a highly effective control strategy, owing to its outstanding dynamic performance. However, the control effectiveness of traditional methods is limited by the machine parameters set in advance, which inevitably reduces the parameter robustness of the method. When machine parameters change due to factors like temperature, the discrepancy between the actual values and the parameters configured in the controller leads to a decline in DPCC performance, and cause system instability. To tackle the challenge of parameter dependence, this paper proposes an adaptive parameter-free model-free deadbeat predictive current control (PF-MFDPCC) method suitable for interior permanent magnet synchronous motors (IPMSM). The method estimates the actual gain parameters based on the sampled current values and reference values, and determines the required harmonic current injection by minimizing torque ripple. First, the relationship of the parameters to be estimated is derived based on a first-order ultra-local model. Then, the optimal harmonic current is injected in the rotor reference frame (RRF), and inductance parameter estimation is achieved using the Recursive Least Squares (RLS) algorithm's online adaptability. This enables parameter-free motor control and significantly suppresses the impact of controller gain mismatches. Specifically, the optimal harmonic current is derived with the aim of reducing torque ripple, and the resulting harmonic current can significantly reduce the adverse effects of injected harmonic current on DPCC performance. Finally, Simulations confirm the efficacy and accuracy of the proposed method. Compared to traditional methods, the proposed method reduces current total harmonic distortion by 23% with controller gain mismatch.