1,3,5-trinitro-1,3,5-triazacyclohexane (RDX) or hexogen, a high-insensitivity explosive, the accurately description of its energy and properties is of fundamental significance in the sense of security and application. Based on the machine learning method, high-dimensional neural network is used to construct potential function of RDX crystal. In order to acquire enough data in neural network learning, based on the four known crystal phases of RDX, the structural global search is performed under different spatial groups to obtain 15199 structure databases. Here in this study, we use nearby atomic environment to build 72 different basis functions as input neurons, in which the 72 different basis functions represent the interaction with nearby atoms for each type of element. Among them, 90% data are randomly set as training set, and the remaining 10% data are taken as test set. To obtain the better training effect, 9 different neural network structures carry out 2000 step iterations at most, thereby the 30-30-10 hidden layer structure has the lower root mean square error (RMSE) after the 1847 iterations compared with the energies from first-principles calculations. Thus, the potential function fitted by 30-30-10 hidden layer network is chosen in subsequent calculations. This constructed potential function can reproduce the first-principles results of test set well, with the RMSE of 59.2 meV/atom for binding energy and 7.17 eV/Å for atomic force. Especially, the RMSE of the four known RDX crystal phases from 1 atm to 6 GPa are 10.0 meV/atom and 1.11 eV/Å for binding energy and atomic force, respectively, indicating that the potential function has a better description of the known structures. Furthermore, we also propose four additional RDX crystal phases with lower enthalpy, which may be alternative crystal phases undetermined in experiment. In addition, based on molecular dynamics simulation with this potential function, the α-phase RDX crystal can stay stable for a few ps, further proving the applicability of our constructed potential function.