The application of deep learning to direction of arrival (DOA) estimation is of great significance in the field of array signal processing. The use of deep learning for DOA estimation of vector hydrophone array usually directly inputs the covariance matrix of the signal as the signal feature into the network, but this method has limitations such as high data requirements and high computational complexity. This paper proposes a DOA estimation method for vector hydrophone array based on a convolutional sparse autoencoder under sparse prior conditions. This method adds an L1 norm regularization term to the convolutional layer of a convolutional autoencoder to achieve sparsity constraints, and establishes a convolutional sparse autoencoder. At the same time, a residual compensation mechanism is introduced to avoid overfitting and loss of details during the training process. Subsequently, the columns of the signal covariance matrix of the vector hydrophone array are treated as under-sampled noisy linear measurements of the spatial spectrum, and are input into a convolutional sparse autoencoder for feature extraction and reconstruction. Finally, the obtained features are used as inputs for training a convolutional neural network to achieve multi-source DOA estimation. Furthermore, to address the shortcomings of classification methods in off-grid situations, we propose a DOA regression estimation method based on the convolutional sparse autoencoder. The simulation results show that under complex conditions such as low signal-to-noise ratio and a small number of snapshots, the classification method proposed in this paper outperforms various deep learning algorithms and traditional algorithms mentioned in the literature in terms of estimation performance. In addition, the proposed regression method can further improve the DOA estimation performance in off-grid scenarios.