Abstract: To overcome the shortcomings of Logistic map, an improved Logistic chaotic map is designed via delayed feedback.Based on the proposed chaotic map, a new image encryption algorithm relative to plain text is proposed. The simulation results show that the encryption algorithm proposed in this paper only needs a round of permutation and diffusion operation to achieve satisfactory encryption effect, and can effectively resist statistical analysis attack, differential attack and selective plain text attack, and exhibits strong robustness.