In this paper, we propose a novel deep learning (DL)-based gridless direction-of-arrival (DOA) estimation method for generalized linear arrays using residual attention network (RAN) and transfer learning (TL). The proposed method can improve the DOA estimation performance in both low and high signal-to-noise ratio (SNR) regions by focusing on the important features in the input and avoiding the problems of gradient vanishing and network degradation. Moreover, we introduce the idea of TL to reduce the complexity and costs of training. The experimental results demonstrate the effectiveness and superiority of our method compared with existing methods.