Abstract: To solve the problem of low security level of encrypted gray image, based on chaotic time series from functional projective synchronization of the hyper-chaotic system and its state observer, the "add modulus pixel diffusion algorithm" was used to encrypt and decrypt gray image. The state observer of the hyper-chaotic system was constructed. First, the state observer of the hyper-chaotic system was conducted by using the state output vector of the hyper-chaotic system, and according to control theory method, the sufficient condition of function projective synchronization was given for the hyper-chaotic system and the state observer. Then, based on chaotic time series of functional projective synchronization, encrypted and decrypted images of gray image were obtained by using the "add modulus pixel diffusion algorithm". Theoretical analysis and numerical simulation show the constructed state observer is correct, the sufficient condition of functional projection synchronization is effective, and there is no significant difference between the encrypted image distribution and the uniform distribution. At the same time, the algorithm is highly sensitive to the key, and has strong ability to resisting attack and has accurate decryption effect.