This paper presents a novel efficient high-resolution two-dimensional direction-of-arrival (2D DOA) estimation method for uniform circular arrays (UCA) using convolutional neural networks. The proposed 2D DOA neural network in the single source scenario consists of two levels. At the first level, a classification network is used to classify the observation region into two subregions (0°, 180°) and (180°, 360°) according to the azimuth angle degree. The second level consists of two parallel DOA networks, which correspond to the two subregions, respectively. The input of the 2D DOA neural network is the preprocessed UCA covariance matrix, and its outputs are the estimated elevation angle to be modified by postprocessing and the estimated azimuth angle. The purpose of the postprocessing is to enhance the proposed method’s robustness to the incident signal frequency. Moreover, in the inevitable array imperfections scenario, we also achieve 2D DOA estimation via transfer learning. Besides, although the proposed 2D DOA neural network can only process one source at a time, we adopt a simple strategy that enables the proposed method to estimate the 2D DOA of multiple sources in turn. Finally, comprehensive simulations demonstrate that the proposed method is effective in computation speed, accuracy, and robustness to the incident signal frequency and that transfer learning could significantly reduce the amount of required training data in the case of array imperfections.