An efficient and simple encryption and compression scheme for digital image is reported in this paper. This scheme is based on the algorithm of the generalized knight's tour, discrete cosine transform and non-linear chaotic maps. In this scheme, according to the structure of compression, confusion and diffusion are attained by methods of the generalized knight's tour and chaotic maps. Firstly, the generalized knight's tour algorithm is utilized to scramble the pixels while the data correlation preserved. Then, the chaotic system is used to generate a pseudorandom permutation to encrypt the part of coefficients from discrete cosine transform for diffusion. Experimental results show that the proposed scheme can gain robust security and a high compression ratio, which indicates that the proposed scheme is practicable.