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Traditional deadbeat predictive current control is an effective control approach, due to its simple concept, easy implementation, and fast dynamic response. However, the parameter mismatch is one of the main problems affecting its wide application. Model-free predictive current control on the basis of the extended state observer (ESO-MFPCC) is an effective solution to the above problem, while the bandwidth limitation in ESO will reduce the control performance. Moreover, because of the voltage limitation of the power converter, in response to load impacts, the motor potentially has poor dynamic performance under the overmodulation region. In order to solve these above problems, model-free predictive current control on the basis of the adaptive sliding mode observer (ASMO-MFPCC) with an overmodulation scheme is proposed. First, the ASMO-MFPCC can preferably improve system parameter robustness without bandwidth limitation. In addition, the vertical method for optimizing dynamic performance in the overmodulation region is proposed, so that the quicker and better dynamic response is obtained between the linear modulation region and the overmodulation region. Finally, the feasibility and effectiveness of the method, carried on a 1-KW surfaced permanent magnet synchronous motor, are verified through the experimental results.