Image encryption is a common way of information protection. However, most of the existing image encryption schemes have been restricted to low transmission efficiency and large memory consumption due to ciphertext redundancy. A high-efficiency and security image algorithm with Block Compressed Sensing (BCS) is designed in this paper to protect image information and reduce redundant data. For a start, the original image is sparsely processed by Discrete Wavelet Transform (DWT), and then pixel positions in the global scope are scrambled by chaotic sequence. Secondly, several image blocks are obtained by dividing scrambled images and sequentially the computational complexity can be cut down. Next, the image blocks are measured by a key-controlled partial Hadamard matrix to reduce the dimension. Finally, image blocks are merged and a proposed Randomly Selected Pixel Diffusion (PSPD) is used to further enhance security performance. Specifically, SHA-512 value of the original image is used for key generation, and then plaintext sensitivity is improved. The pseudo-random sequences that are required for scrambling and diffusion are produced by Chen system and logistic map. Simulation results show that this mechanism has low complexity, higher performance of security compared with others.