Automatic facial action unit (AU) recognition has attracted great attention but still remains a challenging task, as subtle changes of local facial muscles are difficult to thoroughly capture. Most existing AU recognition approaches leverage geometry information in a straightforward 2D or 3D manner, which either ignore 3D manifold information or suffer from high computational costs. In this paper, we propose a novel geodesic guided convolution (GeoConv) for AU recognition by embedding 3D manifold information into 2D convolutions. Specifically, the kernel of GeoConv is weighted by our introduced geodesic weights, which are negatively correlated to geodesic distances on a coarsely reconstructed 3D face model. Moreover, based on GeoConv, we further develop an end-to-end trainable framework named GeoCNN for AU recognition. Extensive experiments on BP4D and DISFA benchmarks show that our approach significantly outperforms the state-of-the-art AU recognition methods.