The design of light emitting diode (LED) solar simulator needs to establish a high accuracy mathematical model with good stability for LED spectra. According to the characteristics of nonlinear LED spectrum mathematical model, a back propagation (BP) neural network optimized by improved genetic algorithm (GA) is proposed to identify LED spectral model. By improving the operator of GA, the convergence effect and the identification accuracy is improved. The improved GA is used to optimize the initial weights and thresholds of BP neural network, which is used to establish reliable LED spectral model. Under different driving current conditions, white and red LED are selected as experimental samples to verify the experiment. Experimental results show that the LED spectrum model is very close to the measured spectrum, and it has higher precision and better universality than other models.