In order to improve the safety and efficiency of image encryption algorithms,a new adaptive algorithm based on quantum Logistic map and 2D discrete wavelet transform (DWT),which combines confusion and diffu-sion,is proposed.In this algorithm,first,the original image is decomposed into low- pass subband and high- pass subband coefficients via the DWT,and the low- pass ones are sorted out by using the quantum Logistic map with random sequences,followed by an inverse DWT to obtain a shuffled image. Then,each pixel of the shuffled image is mixed with the chaotic sequence generated by the quantum Logistic system,and the quantum Logistic system is perturbed to substitute for pixel values adaptively.Thus,better diffusion effect is achieved.Experimental results and performance analysis demonstrate that the proposed algorithm is of large key space,high security and high operation speed,etc.,and that it helps to obtain cipher images with random gray distribution.