Using deep learning (DL) to achieve direction-of-arrival (DOA) estimation is an open and meaningful exploration. Existing DL-based methods achieve DOA estimation by spectrum regression or multi-label classification task. While, both of them face the problem of off-grid errors. In this paper, we proposed a cascaded deep neural network (DNN) framework named as off-grid network (OGNet) to provide accurate DOA estimation in the case of off-grid. The OGNet is composed of an autoencoder consisted by fully connected (FC) layers and a deep convolutional neural network (CNN) with 2-dimensional convolutional layers. In the proposed OGNet, the off-grid error is modeled into labels to achieve off-grid DOA estimation based on its sparsity. As compared to the state-of-the-art grid-based methods, the OGNet shows advantages in terms of precision and resolution. The effectiveness and superiority of the OGNet are demonstrated by extensive simulation experiments in different experimental conditions.