In order to determine the parameters of the JWL equation of state for unreacted explosives， a method to determine the JWL parameters by using the BP neural network-Genetic Algorithm （BP-GA Algorithm） and the shock Hugoniot was proposed. Firstly， BP neural network is trained to fit the nonlinear system composed of different JWL parameters， and then Genetic Algorithm is used to search the set of JWL parameters with the largest fitness value. The results show that the JWL parameters can be determined by the BP-GA Algorithm when the initial density， detonation velocity， Hugoniot parameters C₀ and S are known. The p-v curves of eight kinds of unreacted explosives determined by BP-GA Algorithm are consistent with those determined by test data， and the R² of eight p-v curves are not less than 0.9995， which proves the high accuracy of BP-GA algorithm.