The use of medical imaging as an effective means of diagnosing diseases has become crucial in the recent past. As all these images are communicated through networks, it’s crucial to provide sufficient protection against unauthorized access. There are several ways in which these images can be protected, and encryption is among some of the best methods available. Encryption algorithms typically involve two primary steps: confusion and diffusion, making it secure and safe. This study proposes a new chaos-based encryption algorithm accompanied by the novel Logistic-Chua Map to maintain privacy of medical images transmission through digital media. Thus, based on the characteristics of the LC Map, a robust Substitution box (S-box) with parameters a = 2.15,b = 0.08,c = 0.03, and r ranging from 0.5 to 5.5. generated by means of the proposed Algorithm. The first algorithm searches for these parameters systematically and strived for an S-box which provides increase in cryptographic strength by means of non-linear substitutions. The S-box is used in the second algorithm to encrypt images with medical data, with 8-bytes key size and the block size of 16 × 16. The encryption process is done via pixel-wise and block-wise substitution, which ensures that there is enough diffusion and confusion. These encrypted images are tested for statistical properties of the data, sensitivity to initial conditions, and against various attacks. The results highlighted that the proposed scheme is effective in protecting medical images and a more efficient solution of secure transmission of medical images.