S-box structures used in the encryption architecture are of great importance for constructing powerful block encryption systems, which hold an important place in modern cryptology. The design of S-boxes with sound cryptographic characteristics is of utmost importance for constructing powerful encryption systems. In this study, an S-box design algorithm based on time-delay chaotic systems is proposed. The proposed algorithm is considered relative to other algorithms in the literature as more useful according to such criteria as simplicity and efficient implementation. Theoretical analysis and computer simulations demonstrated that the proposed algorithm meets all the performance requirements for the S-box design criteria, and also verified the efficient and practical structure of the algorithm.