Compressed sensing (CS), as a signal processing technique, is often used to acquire and reconstruct a sparse signal. It can decrease the difficulty of acquiring signal while increase the difficulty of reconstructing the signal. Recently, block-based intra-prediction algorithms are widely used to further increase the compression ratio of images by using the information of neighboring blocks to predict the current block. However, it is hard to increase the speed by parallel processing due to the dependency among the blocks. Meanwhile, the reconstruction of compressed sensing images is time consuming. A reconstruction algorithm using Zigzag ordering-based parallelism is proposed in this paper to solve these problems. Besides, based on the feature of the chosen sensing matrix, a new method with higher efficiency for choosing the first candidate list in the reconstruction procedure was presented in this paper. The experimental results demonstrated that the proposed algorithm speedups the baseline algorithm for 3.26 to 7.13 times. And the quality of the reconstructed images is not changed. Thus, it is a promising solution for fast reconstruction of compressed images
