The purpose of this paper is to present the design, the math model, the result simulation, and discussion of a back-propagation neural network (BB-NN) for a two-mass system. The aim is to controller design simply and control the actual angular speed matching with the reference angular speed, lead to reduces the resonance oscillation at shaft between motor and load. BP-NN controller is designed based on the backward propagation of errors and training artificial neural networks are used in combination with an optimized method as gradient descent. This method calculates the gradient of the loss function with all the relevant weighting in the neural network. This gradient is fed into the optimization method, which uses it to update the weights, to minimize the loss function. The efficiency of the BB-NN control method is verified by HIL real-time simulation.