A reverse design of a phononic crystal structure based on conditional autoencoder is proposed in response to the low-frequency vibration control issue in the sonar dome. The designed phononic crystal structure，featuring a band gap in the target frequency band，can be used as the sandwich structure's core layer，providing a new idea for the vibroacoustic characteristics management of the sonar dome. Firstly，many phononic crystal periodic units are randomly generated，and two strategies are proposed to expand the number of samples with band gaps in the target frequency band. To solve the problem of low efficiency of batch calculation of the phononic crystal structure band gap by Finite Element Software，a convolutional neural network is trained to identify whether the phononic crystal has band gaps. Finally，the phononic crystal structure and band gap distribution are used as the training condition autoencoder. The results show that the convolutional neural network has a high recognition accuracy of the band gap of the structure，which is up to 89%. The conditional autoencoder can learn the axisymmetric structure of the artificial periodic structure. The generated artificial periodic structure is only a few pixels different from the original structure. The band gap error between the generated structure and the original structure is less than 1%，indicating that this method can be applied to the reverse design of the phononic crystal structure.