Images are now widely used in medical diagnosis. To protect the privacy of patients, the security of image information has been becoming more and more important. In order to increase the security of digital image encryption results, this paper proposes a new image encryption algorithm based on improved Logistic mapping, Arnold mapping, Kent mapping and wavelet transform. The Arnold mapping and the wavelet transform were used to shuffle image pixels and the Kent mapping was introduced to generate the control parameters in the Arnold mapping. The improved Logistic mapping for pseudo-random number generation and have done xor operation between the pixel value and the key value generated by the improved Logistic mapping. By analyzing and testing the secret key space, the information entropy, the correlation coefficient and the plaintext sensitivity, experimental results show that the algorithm has the advantages of simple structure, high security and is easier to apply.