In this article, a novel sensitive encryption scheme to secure the digital images based on the Zaslavsky chaotic map is proposed. We employ the Zaslavsky chaotic map as a pseudo-random generator to produce the key encryption of the proposed image cryptosystem. The cipher structure has been chosen based on permutation-diffusion processes, where we adopt the classic permutation substitution network, which ensures both confusion and diffusion properties for the encrypted image. Our proposed algorithm has high sensitivity in plain image and the secret key. Moreover, the results show that the characteristics of our approach have excellent performance, with high scores (NPRC = 99.61%, UACI = 33.47%, entropy (CipherImage)  8, and correlation coefficient  0). Experimental results have been studied and analyzed in detail with various types of security analysis. These results demonstrate that our proposed cryptosystem has highly satisfactory security performance and can withstand various attacks compared to state-of-the-art methods.