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Deep learning based methods, such as Convolution Neural Network (CNN), have demonstrated their efficiency in hyperspectral image (HSI) classification. These methods can automatically learn spectral-spatial discriminative features within local patches. However, for each pixel in an HSI, it is not only related to its nearby pixels but also has connections to pixels far away from itself. Therefore, to incorporate the long-range contextual information, a deep fully convolutional network (FCN) with an efficient non-local module, named ENL-FCN, is proposed for HSI classification. In the proposed framework, a deep FCN considers an entire HSI as input and extracts spectral-spatial information in a local receptive field. The efficient non-local module is embedded in the network as a learning unit to capture the long-range contextual information. Different from the traditional non-local neural networks, the long-range contextual information is extracted in a specially designed criss-cross path for computation efficiency. Furthermore, by using a recurrent operation, each pixel's response is aggregated from all pixels of HSI. The benefits of our proposed ENL-FCN are threefold: 1) the long-range contextual information is incorporated effectively, 2) the efficient module can be freely embedded in a deep neural network in a plug-and-play fashion, and 3) it has much fewer learning parameters and requires less computational resources. The experiments conducted on three popular HSI datasets demonstrate that the proposed method achieves state-of-the-art classification performance with lower computational cost in comparison with several leading deep neural networks for HSI.