We propose a general and fully automatic framework for 3D facial expression recognition by modeling sparse representation of conformal images. According to Riemann Geometry theory, a 3D facial surface S embedded in reals3, which is a topological disk, can be conformally mapped to a 2D unit disk D through the discrete surface Ricci Flow algorithm. Such a conformal mapping induces a unique and intrinsic surface conformal representation denoted by a pair of functions defined on D, called conformal factor image (CFI) and mean curvature image (MCI). As facial expression features, CFI captures the local area distortion of S induced by the conformal mapping; MCI characterizes the geometry information of S. To model sparse representation of conformal images for expression classification, both CFI and MCI are further normalized by a Möbius transformation. This transformation is defined by the three main facial landmarks (i.e. nose tip, left and right inner eye corners) which can be detected automatically and precisely. Expression recognition is carried out by the minimal sparse expression-class-dependent reconstruction error over the conformal image based expression dictionary. Extensive experimental results on the BU-3DFER dataset demonstrate the effectiveness and generalization of the proposed framework.