In recent years, vector-based machine learning algorithms, such as random forests, support vector machines, and 1-D convolutional neural networks, have shown promising results in hyperspectral image classification. Such methodologies, nevertheless, can lead to information loss in representing hyperspectral pixels, which intrinsically have a sequence-based data structure. A recurrent neural network (RNN), an important branch of the deep learning family, is mainly designed to handle sequential data. Can sequence-based RNN be an effective method of hyperspectral image classification? In this paper, we propose a novel RNN model that can effectively analyze hyperspectral pixels as sequential data and then determine information categories via network reasoning. As far as we know, this is the first time that an RNN framework has been proposed for hyperspectral image classification. Specifically, our RNN makes use of a newly proposed activation function, parametric rectified tanh (PRetanh), for hyperspectral sequential data analysis instead of the popular tanh or rectified linear unit. The proposed activation function makes it possible to use fairly high learning rates without the risk of divergence during the training procedure. Moreover, a modified gated recurrent unit, which uses PRetanh for hidden representation, is adopted to construct the recurrent layer in our network to efficiently process hyperspectral data and reduce the total number of parameters. Experimental results on three airborne hyperspectral images suggest competitive performance in the proposed mode. In addition, the proposed network architecture opens a new window for future research, showcasing the huge potential of deep recurrent networks for hyperspectral data analysis.