Background subtraction of videos has been a fundamental research topic in computer vision in the past decades. To alleviate the computation burden and enhance the efficiency, background subtraction from online compressive measurements has recently attracted much attention. However, current methods still have limitations. First, they are all based on matrix modeling, which breaks the spatial structure within video frames. Second, they generally ignore the complex disturbance within the background, which reduces the efficiency of the low-rank assumption. To alleviate this issue, we propose a tensor-based online compressive video reconstruction and background subtraction method, abbreviated as NIOTenRPCA, by explicitly modeling the background disturbance in different frames as nonidentical but correlated noise. By virtue of such sophisticated modeling, the proposed method can well adapt to complex video scenes and, thus, perform more robustly. Extensive experiments on a series of real-world video datasets have demonstrated the effectiveness of the proposed method compared with the existing state of the arts. The code of our method is released on the website: https://github.com/crystalzina/NIOTenRPCA.