Recent deep neural networks based methods have achieved state-of-the-art performance on various facial expression recognition tasks. Despite such progress, previous researches for facial expression recognition have mainly focused on analyzing color recording videos only. However, the complex emotions expressed by people with different skin colors under different lighting conditions through dynamic facial expressions can be fully understandable by integrating information from multi-modal videos. We present a novel method to estimate dimensional emotion states, where color, depth, and thermal recording videos are used as a multi-modal input. Our networks, called multi-modal recurrent attention networks (MRAN), learn spatiotemporal attention volumes to robustly recognize the facial expression based on attention-boosted feature volumes. We leverage the depth and thermal sequences as guidance priors for color sequence to selectively focus on emotional discriminative regions. We also introduce a novel benchmark for multi-modal facial expression recognition, termed as multi-modal arousal-valence facial expression recognition (MAVFER), which consists of color, depth, and thermal recording videos with corresponding continuous arousal-valence scores. The experimental results show that our method can achieve the state-of-the-art results in dimensional facial expression recognition on color recording datasets including RECOLA, SEWA and AFEW, and a multi-modal recording dataset including MAVFER.