The work aims to propose an image encryption algorithm combining quantum Logistic chaotic mapping with 3D Arnold chaotic mapping to improve the complexity of image encryption. Firstly, the quantum Logistic chaotic mapping was used to generate the pseudo random sequence for the scrambling with the plain text as a whole, and then an integer sequence was generated with the 3D Arnold chaotic mapping. The diffusion operation was carried out with the scrambled ciphertext. Through simulation experiments, the correlation coefficient of encrypted image was close to 0, the test values of NPCR and UACI of key sensitivity were approximately equal to 99.60 and 33.4, respectively, and the test result of information entropy was approximately equal to 7.999, which were very close to the theoretical values. The encryption algorithm fully reflects the nonlinear mechanical property of high complexity of quantum chaotic mapping. Based on the simulation experiment, the encryption algorithm has such advantages as large key space, strong sensitivity and good security.