Image hashing is a technique to map a digital image into a content-based and short binary code. It has the properties of robustness, security, compactness and one-wayness, which has been widely applied in the field of image authentication and identification. Here, a robust image hashing algorithm based on block compressed sensing is proposed, using the characteristics of secure computation and linear operation in the sampling stage. In the proposed algorithm, the input image is partitioned into sub-blocks. For each sub-block, random projection is applied to it based on the theory of compressed sensing, and a measurement vector can be obtained under the control of the secret key. Then each measurement vector is quantized as one bit and finally a binary hash value can be obtained whose length can be adjusted by the strategy of image partition. Experimental results show that the proposed algorithm has satisfied performance in robustness, security and speed.