Compressed sensing is a novel technology to acquire and reconstruct signals below the Nyquist rate, and has great potential in image and video acquisition to explore the data redundancy and to significantly reduce the number of sampled data. In this paper, we explore the temporal redundancy in videos, and propose a block-based adaptive framework for compressed video sampling. It addresses the independent movement of different regions in a video, classifies blocks into different types depending on their inter-frame correlation, and adjusts the sampling and reconstruction strategies accordingly. Our framework also considers the diverse texture complexity of different regions, and adaptively adjusts the number of measurements collected for each region based on their sparsity. Our simulation results show that the proposed framework reduces the number of sampled measurements by 52% to 80% while still satisfying the quality constraint on the reconstructed frames. Compared to prior works, our proposed scheme improves the quality of the reconstructed frames and achieves a 0.8dB to 5.4dB gain in the average PSNR.