In recent video-based point cloud compression (V-PCC), 3D point clouds are projected onto 2D images and compressed by High-Efficiency Video Coding (HEVC). However, HEVC was originally designed for natural visual signals, which is a suboptimal framework for point clouds. Therefore, there are still problems in geometry information compression in V-PCC: (1) The distortion based on the sum of squared error (SSE) in the existing rate-distortion optimization (RDO) is inconsistent with the geometric quality measurement; (2) The existing prediction cannot explore the fixed relationship between the corresponding far layer and near layer depth, which means that the far layer depth can be always not less than the corresponding near layer depth. In this paper, we present an efficient geometry surface coding (EGSC) method for V-PCC to address the problems. Firstly, an error projection (EP) model is designed to establish the relationship between the SSE-based distortion and the geometry quality metric. Secondly, an EP-based RDO is employed to improve the geometry information compression by estimating the point normals with gradients. Finally, an occupancy-map driven scheme is proposed to improve the prediction accuracy of merge modes. Experimental results show that the proposed method achieves an average of over 10% bit-rate saving compared with the V-PCC reference software.