Aiming at the inherent hysteresis nonlinearity of piezoelectric ceramics, a feedforward compensation control system based on the deep neural network (DNN) is designed in this paper. The system consists of one input layer, seven hidden layers and one output layer. The experimental results show that the displacement linearity error of piezoelectric ceramics reaches 8.91 μm in the open loop condition. After applying neural network feedforward compensation, the maximum displacement error of piezoelectric ceramics is reduced to 80 nm, and the steady-state error is ±20 nm. Further tests show that the maximum error of the system is less than 100 nm at the input frequency of 10~100 Hz, and the root mean square error is 0.01 μm, which verifies that the deep neural network can accurately compensate the dynamic hysteresis and nonlinearity of piezoelectric ceramics and has good frequency generalization ability.