A method combining a back propagation (BP) neural network algorithm with the artificial bee colony algorithm is introduced, and the design of multi-pump Raman fiber amplifier is optimized by this method. The best learning model is determined by studying the numbers of hidden layers and neural nodes in the multilayer BP neural network, which can accurately reflect the mapping relationships of the pump wavelength and pump power with the distribution of Raman net gain, and can replace the traditional method for solving the Raman coupled wave equation. At the same time, in order to improve the flatness of the gain spectrum, the artificial bee colony algorithm is used to optimize the pump parameters and the optimal pump wavelength and pump power are obtained. The simulation results show that when the trained BP neural network model is added into the artificial bee colony algorithm, the desired gain performance of the studied Raman amplifier is achieved. Moreover, the maximum error between the target value and the predicted value is less than 0.29 dB. This design scheme provides a new method and idea for the study of Raman fiber amplifiers.