We proposed a neural network energy function for the optimal graph partitioning and its optimization method using Boltzmann Machine. We composed a Boltzmann Machine with the proposed neural network energy function, and the simulation results show that we can obtain an optimal solution with the energy function parameters of A=50, B=5, c=14 and D=10, at the Boltzmann Machine parameters of To=80 and ulcorner0.07 for a 6-node 3-partition problem. As a result, the proposed energy function and optimization parameters are proved to be feasible for the optimal graph partitioning.