A fractal interpolation algorithm based on adaptive mutation Particle Swarm Optimization (PSO) was proposed aiming at the interpolation problem of a large number of continuous missing data in wind speed data of wind farms. First, the mutation factor was introduced into the particle swarm optimization algorithm to enhance the diversity of particles and the search accuracy of the algorithm. Second, the optimal value of the vertical scaling factor in the fractal interpolation algorithm was obtained by the adaptive mutation particle swarm optimization algorithm. Finally, two datasets with different trends and change characteristics were analyzed by fractal interpolation, and the proposed algorithm was compared with Lagrange interpolation and cubic spline interpolation. The results show that fractal interpolation is not only able to maintain the overall fluctuation characteristics and local characteristics of wind speed curve, but also is more accurate than the traditional interpolation methods. In the experiment based on Dataset A, the Root Mean Square Error (RMSE) of fractal interpolation was reduced by 66.52% and 58.57% respectively compared with those of Lagrange interpolation and cubic spline interpolation. In the experiment based on Dataset B, the RMSE of fractal interpolation was decreased by 76.72% and 67.33% respectively compared with those of Lagrange interpolation and cubic spline interpolation. It is verified that fractal interpolation is more suitable for the interpolation of wind speed time series with strong fluctuation and continuous missing data.