Multiview video plus depth is one of the mainstream representations of 3D scenes in emerging free viewpoint video, which generates virtual 3D synthesized images through a depth-image-based-rendering (DIBR) technique. However, the inaccuracy of depth maps and imperfect DIBR techniques result in different geometric distortions that seriously deteriorate the users’ visual perception. An effective 3D synthesized image quality assessment (IQA) metric can simulate human visual perception and determine the application feasibility of the synthesized content. In this paper, a no-reference IQA metric based on visual-entropy-guided multi-layer features analysis for 3D synthesized images is proposed. According to the energy entropy, the geometric distortions are divided into two visual attention layers, namely, bottom-up layer and top-down layer. The feature of salient distortion is measured by regional proportion plus transition threshold on a bottom-up layer. In parallel, the key distribution regions of insignificant geometric distortion are extracted by a relative total variation model, and the features of these distortions are measured by the interaction of decentralized attention and concentrated attention on top-down layers. By integrating the features of both bottom-up and top-down layers, a more visually perceptive quality evaluation model is built. Experimental results show that the proposed method is superior to the state-of-the-art in assessing the quality of 3D synthesized images.