A 3D model based approach for a face representation and recognition algorithm has been investigated as a robust solution for pose and illumination variation. Since a generative 3D face model consists of a large number of vertices, a 3D model based face recognition system is generally inefficient in computation time and complexity. In this paper, we propose a novel 3D face representation algorithm based on a pixel to vertex map (PVM) to optimize the number of vertices. We explore shape and texture coefficient vectors of the 3D model by fitting it to an input face using inverse compositional image alignment (ICIA) to evaluate face recognition performance. Experimental results show that the proposed face representation and recognition algorithm is efficient in computation time while maintaining reasonable accuracy.