Large computational burden, time delay, and the necessity for precise modeling accuracy are the three main challenges for Finite Control Set-Model Predictive Control (FCS-MPC) in single-phase grid-tied inverters. To solve these issues, a twisted parameter scheme is proposed for the single-phase inverter in this article. Firstly, the law regarding the influence of the model parameter on the current total harmonic distortion (THD) is outlined, emphasizing that a decrease in the inductance parameter leads to a corresponding reduction in current THD. Second, a linear observer is constructed to identify the actual value of inductance and resistance, and an RBF-GA (Radial Basis Function neural network-Genetic Algorithm) scheme is used to obtain the optimal twisted parameter. Subsequently, the efficacy of the proposed methods was verified utilizing MATLAB/Simulink simulations, with further validation conducted through hardware-in-the-loop (HIL) experiments performed on Speedgoat performance real-time target machines. Simulation and experimental results demonstrate that within a specific range, decreasing the inductance parameter can significantly improve the quality of the current. Furthermore, the proposed method outperforms the traditional delay compensation method by reducing computational complexity, minimizing prediction error, and decreasing the number of switching transitions.