In response to the problem that the proportion of power electronic devices in the new power system is increasing, leading to intensified nonlinear responses and a significant increase in harmonic components of single-phase grounding fault currents, and traditional arc suppression methods are difficult to effectively suppress the arc, this paper proposed an arc suppression method based on fractional order model predictive control(FOMPC). Firstly, the traditional inductors in the double-linked H-bridge were replaced with fractional-order inductors of different orders. Secondly, the corresponding order model predictive control method was adopted to compensate for the fault residual current based on the principle of minimizing the current tracking error, thereby achieving effective arc suppression. Finally, the performance of the method was verified through hardware-in-the-loop experiments. The results show that using the appropriate order FOMPC for arc suppression has superior performance in response speed and arc suppression effect. The integration of fractional calculus theory with active arc suppression inverters and its control can improve the response speed and reduce the fault current, providing a reference for fault suppression in power electronicized power grids.