This paper focuses on non-convex composite optimization problems and improves the mirror inertial forward-reflected-backward (i*FRB) algorithm by introducing an extrapolation step, proposing a mirror inertial modified forward-reflected-backward method (i*MFRB). This work extends the application of the forward-backward splitting algorithm with an extrapolation step to non-convex scenarios and offers a more concise proof approach for the forward-reflected-backward splitting algorithm. By constructing an appropriate and simple value function, the convergence of the algorithm's function values is established. Furthermore, by combining the Kurdyka-ojasiewicz property, the convergence of the algorithm's iterative sequence is proved. The proposed algorithm is applied to a class of non-convex feasibility problems, and a corresponding sub-problem solving approach is designed. Finally, numerical experiments are conducted to compare the i*MFRB splitting algorithm with existing similar algorithms in high-dimensional cases.