In 3D video systems, imperfect depth images often induce annoying temporal noise, e.g., flickering, to the synthesized video. However, the quality of synthesized view is usually measured with peak signal-to-noise ratio or mean squared error, which mainly focuses on pixelwise frame-by-frame distortion regardless of the obvious temporal artifacts. In this paper, a novel full reference synthesized video quality metric (SVQM) is proposed to measure the perceptual quality of the synthesized video in 3D video systems. Based on the proposed SVQM, an improved rate-distortion optimization (RDO) algorithm is developed with the target of minimizing the perceptual distortion of synthesized view at given bit rate. Then, the improved RDO algorithm is incorporated into the 3D High Efficiency Video Coding (3D-HEVC) software to improve the 3D depth video coding efficiency. Experimental results show that the proposed SVQM metric has better consistency with human perception on evaluating the synthesized view compared with the state-of-the-art image/video quality assessment algorithms. Meanwhile, this SVQM metric maintains low complexity and easy integration to the current video codec. In addition, the proposed SVQM-based depth coding scheme can achieve approximately 15.27% and 17.63% overall bit rate reduction or 0.42- and 0.46-dB gain in terms of SVQM quality score on average as compared with the latest 3D-HEVC reference model and the state-of-the-art depth coding algorithm, respectively.