To reduce the dependence of the finite control set model predictive control performance of grid-connected inverters on system model parameters, a model-free predictive control method for grid-connected inverters based on an adaptive sliding mode observer is proposed. Firstly, based on the ultra-local model theory, an adaptive sliding mode observer is designed to accurately observe the total disturbance of the system, effectively avoiding the dependence of traditional methods on precise model parameters and enhancing the robustness and anti-interference ability of the system. To optimize the system architecture, an extended Kalman filter is introduced to replace the grid-side voltage sensor, providing key parameters for model-free prediction by real-time estimation of the grid-side voltage state, while reducing the complexity of system design. To address the performance degradation caused by control delay in digital controllers, an improved delay compensation method based on the first-order linear extrapolation is proposed. By using historical current data to predict the system state after delay, the compensation current is used for the next cycle prediction, improving the real-time performance and accuracy of current tracking. Finally, a simulation model and an experimental prototype are established for comparison and analysis with traditional methods. Experimental results show that, compared with the traditional model predictive control strategy, the proposed method reduces the total harmonic distortion rate of the grid-connected current by 36.67% when the inductance suddenly increases and by the sudden 47.84% decrease. When the reference current undergoes a sudden change, the system dynamic response speed is increased by 21.78%, and the total harmonic distortion rate of the current in steady-state operation is as low as 2.37%, meeting the grid connection standards. The proposed strategy effectively reduces the negative impact of model parameter dependence and control delay through multi-module collaborative optimization, providing a reliable control solution for the efficient and stable operation of grid-connected inverters.