In order to solve the problem of difficulty of both the high perception robustness and tampering identification rate in the current image Hash algorithm, the compact image Hash algorithm based on data projection dimension reduction mechanism and fuzzy symmetric local binary pattern is proposed. The generated Hash has a fixed length by introducing the bilinear interpolation mechanism to preprocess the image. And the pretreatment image is transformed into the secondary image by the log polar transformation. The secondary image is smoothed by Gabor filter. The fuzzy symmetric local binary pattern operator is designed based on the fuzzy theory. And the compact intermediate Hash sequence is got by defining the data projection dimension reduction mechanism. The image Hash is generated by diffusing the bit Hash based on designing the one-dimensional combined chaotic map. The similarity between the original image and the image of the receiving end is estimated by introduction the Hamming distance and decision threshold to finish the authentication of image. Testing data show that this algorithm has stronger perception robust and sensitivity with tighter Hash length than the current image Hash technologies.