The linear synchronous motor is analyzed through the winding function theory, and a fault diagnosis method of linear synchronous motor based on convolutional neural network (CNN) is proposed. Starting from the mathematical model of the linear synchronous motor, the normal state and turn-to-turn fault state of the motor are analyzed based on the winding function theory. The short-circuit fault state is simulated, and the fast Fourier transform (FFT) of the current waveform is performed to obtain data sets of different states. This method uses the GoogLeNet network structure in CNN to achieve the characteristics of not increasing the amount of calculation while maintaining the dimension of the network space. The data sets are then input into the network model for fault diagnosis. Simulation results show that the GoogLeNet network structure reaches over 96.5% recognition rate for the short-circuit fault of the armature winding of linear synchronous motor.