In order to improve the generalization ability，convergence speed and reduce the error of the fuzzyneural network，the method of using momentum gradient descent algorithm and ＲMSprop optimization algorithm to optimize the fuzzy neural network is proposed． The adaptive process of parameter adjustment of the neural network is studied and designed． Ｒegular terms are added to the cost function to update the parameters，and the convergence speed of the fuzzy neural network is guaranteed． The fitting effect and error between the predicted output and the actual output are compared． The two optimization algorithms of fuzzy neural network are applied to output prediction of non-linear function approximation，Mackey-Glass chaotic time series and water quality grade evaluation． The experimental results show that the error and fitting effect of ＲMSprop's predicted output and actual output are better than that of momentum gradient descent algorithm．