Facial action unit (AU) intensity estimation aims to measure the intensity of different facial muscle movements. The external knowledge such as AU co-occurrence relationship is typically leveraged to improve performance. However, the AU characteristics may vary among individuals due to different physiological structures of human faces. To this end, we propose a novel geometry-guided representation learning (G2RL) method for facial AU intensity estimation. Specifically, our backbone model is based on a heatmap regression framework, where the produced heatmaps reflect rich information associated with AU intensities and their spatial distributions. Besides, we incorporate the external geometric knowledge into the backbone model to guide the training process via a learned projection matrix. The experimental results on two benchmark datasets demonstrate that our method is comparable with the state-of-the-art approaches, and validate the effectiveness of incorporating external geometric knowledge for facial AU intensity estimation.