Variants of deep networks have been widely used for hyperspectral image (HSI)-classification tasks. Among them, in recent years, recurrent neural networks (RNNs) have attracted considerable attention in the remote sensing community. However, complex geometries cannot be learned easily by the traditional recurrent units [e.g., long short-term memory (LSTM) and gated recurrent unit (GRU)]. In this article, we propose a geometry-aware deep recurrent neural network (Geo-DRNN) for HSI classification. We build this network upon two modules: a U-shaped network (U-Net) and RNNs. We first input the original HSI patches to the U-Net, which can be trained with very few images and obtain a preliminary classification result. We then add RNNs on the top of the U-Net so as to mimic the human brain to refine continuously the output-classification map. However, instead of using the traditional dot product in each gate of the RNNs, we introduce a Net-Gated GRU that increases the nonlinear representation power. Finally, we use a pretrained ResNet as a regularizer to improve further the ability of the proposed network to describe complex geometries. To this end, we construct a geometry-aware ResNet loss, which leverages the pretrained ResNet's knowledge about the different structures in the real world. Our experimental results on real HSIs and road topology images demonstrate that our approach outperforms the state-of-the-art classification methods and can learn complex geometries.