The control performance of deadbeat predictive current control (DPCC) depends on machine parameters and degrades with inaccurate values. Its parameter robustness worsens at high speed due to low switching-to-fundamental frequency ratios (SFRs). In this paper, an accurate discrete machine model suitable for high-speed permanent magnet synchronous machine (PMSM) and low SFR is first constructed, based on which an accurate discrete incremental model with the advantage of self-elimination of flux linkage is then derived and the incremental model-based DPCC for high-speed PMSM drives is proposed. The steady-state current control performance under parameter mismatch is analytical analyzed for the incremental model-based DPCC. It is found that steady-state current control accuracy is independent of parameter mismatch. Extensive simulations on a high-speed PMSM prototype have been conducted to verify the effectiveness of the proposed incremental model-based DPCC for high-speed PMSMs and its parameter robustness. By comparisons to the conventional discrete dq-axis voltage model-based DPCC and flux tracking-based DPCC, it is concluded that the incremental model-based DPCC exhibits good steady-state control robustness under all parameter mismatches while its transient performance and stability under inductance mismatch deteriorate more significantly with large oscillation and dq-axis coupling.