This study aims to investigate the challenges associated with current control for the switched reluctance motor (SRM) in the presence of model nonlinearity, complex model mismatches, and sampling delay. To address these issues, we introduce a novel composite predictive current control scheme that seamlessly integrates nonlinear model predictive control (NMPC) and high-order disturbance observer (HODO). Initially, a HODO is designed to estimate the rapidly time-varying disturbance and its derivative, enabling the derivation of the disturbance preview information. Subsequently, a composite prediction model is formulated for NMPC control design, incorporating the disturbance estimation-based delay compensation and disturbance preview information. The proposed composite controller can effectively counteract the detrimental effects of sampling delay and model mismatches simultaneously. The efficacy of the proposed controller is validated through simulations and comparisons with the existing control method.