To address the high sensitivity to model-parameter mismatch, the heavy computational burden caused by periodic optimization, and the degradation of grid-current quality induced by digital control delay in conventional finite-control-set model predictive control, an adaptive event-triggered model-free predictive control strategy is proposed for grid-connected inverters. A model-free voltage-vector evaluation function is constructed by taking the grid-current tracking error as the sliding-mode variable. A zero-vector bias and a secondary switching-state screening mechanism are introduced to balance dynamic response, steady-state ripple suppression, and switching-loss reduction. Furthermore, a composite event-triggering mechanism incorporating adaptive error thresholds, the sliding-mode reaching direction, and grid-voltage variations is developed to enable on-demand voltage-vector optimization. A recursively updated current-increment lookup table with a forgetting factor is employed to compensate for the one-sample control delay through state extrapolation. Simulation results show that, when the filter inductance is reduced to 50% of its nominal value, the total harmonic distortion of the grid current achieved by the proposed method is 2.29%, which is 42.75% and 10.89% lower than that of conventional finite-control-set model predictive control and 10.89% lower than that of current-difference-based model-free predictive control, respectively. Stable operation is also maintained under conditions of grid-voltage sag, voltage unbalance, background harmonics, and weak-grid conditions. Experimental results demonstrate that, under inductance mismatch, the total harmonic distortion of the grid current is 2.79%, the settling time following a reference-current step change is 0.582 ms, the number of online optimization operations is reduced by 60.54%, and the average execution time is reduced to 10.41 μs. The secondary switching-state screening mechanism reduces the average switching frequency and switching loss by 12.88% and 12.09%, respectively, while the delay compensation decreases the total harmonic distortion of the grid current from 2.62% to 2.38%. These results demonstrate that the proposed strategy effectively improves parameter robustness, dynamic response, grid-current quality, and real-time computational performance, confirming its potential for practical engineering applications.