Currently, great numbers of efforts have been put into improving the effectiveness of 3D model quality assessment (3DQA) methods. However, little attention has been paid to the computational costs and inference time, which is also important for practical applications. Unlike 2D media, 3D models are represented by more complicated and irregular digital formats, such as point cloud and mesh. Thus it is normally difficult to perform an efficient module to extract quality-aware features of 3D models. In this paper, we address this problem from the aspect of projection-based 3DQA and develop a no-reference (NR) \underline{E}fficient and \underline{E}ffective \underline{P}rojection-based \underline{3D} Model \underline{Q}uality \underline{A}ssessment (\textbf{EEP-3DQA}) method. The input projection images of EEP-3DQA are randomly sampled from the six perpendicular viewpoints of the 3D model and are further spatially downsampled by the grid-mini patch sampling strategy. Further, the lightweight Swin-Transformer tiny is utilized as the backbone to extract the quality-aware features. Finally, the proposed EEP-3DQA and EEP-3DQA-t (tiny version) achieve the best performance than the existing state-of-the-art NR-3DQA methods and even outperforms most full-reference (FR) 3DQA methods on the point cloud and mesh quality assessment databases while consuming less inference time than the compared 3DQA methods.