Traditional numerical methods often struggle to handle time-fractional derivatives effectively, so new numerical methods are required for time-fractional diffusion equations. To solve multi-time fractional diffusion equations efficiently, based on Hermitian and skew-Hermitian splitting (HSS) iterative methods (a unique solution converging to a system of linear equations), new parameters are introduced, and relaxation techniques of the iterative method are combined to accelerate the HSS iterative method. A new extrapolated HSS iterative method is proposed, and its Wilson-like element structure is analyzed. Using the special properties of the element and fractional derivative processing, the super-approximation results are derived, and the super-convergence estimates are derived by interpolation post-processing technology. The test results show that the minimum error of this method is 0.15 %, and the error is small.