Video Quality Assessment (VQA) for windowed six Degree of Freedom (windowed-6DoF) synthesized viewpoints is conducive to the development and broadcasting of 6DoF immersive video system. To explore this new field, we propose the subjective and objective VQA studies for windowed-6DoF synthesized videos. Stage one, a pioneering windowed-6DoF synthesized video quality database with compressed distortion, rendering distortion, and viewing path discomfort are presented, in which overall 128 videos are synthesized from four sequences with different distortion combinations. Stage two, a no-reference objective VQA method is proposed. Firstly, the video is converted into one traditional spatio-temporal domain (XY-T domain) and two new spatio-temporal domains (XT-Y and TY-X domains). Secondly, the emerging rendering distortion and viewing path discomfort are measured in the XT-Y and TY-X domains based on their respective characteristic statistical models, and the common compressed distortion is measured in XY-T domain. Thirdly, the image numbers of new domains are accurately determined through optical flow based depth estimation. Finally, the regression model plus weighting strategy is used to obtain the ultimate quality score of windowed-6DoF synthesized video. Experimental results on three synthesized video databases illustrate that the proposed objective NR VQA method has a good performance in evaluating various synthesized videos, compared with other classic and state-of-the-art 2D/3D IQA/VQA metrics.