Taking advantage of the global optimization of the black-winged kite optimization algorithm, a numerical solution of the fractional order Riccati differential equation based on Haar wavelet function approximation and the black-winged kite optimization algorithm is proposed. Combining Haar wavelet gives the general form of numerical solution of fractional order Riccati differential equation, the original problem is transformed into a single-objective optimization problem with the approximation function to be coefficients as variables, and then solved by the black-winged kite optimization algorithm. The Haar wavelet approximate solution of the fractional order Riccati differential equation is obtained. The error estimation and convergence analysis of the method based on Haar wavelet function to simulate the solution function of the equation are performed, and the stability is evaluated using the optimization performance ratio. The accuracy and stability of the method are demonstrated by comparing the results with those obtained by existing numerical methods.