In this paper, we propose an algorithm for the construction of substitution-box through a linear recurrence relation. S-box is considered as the building block of block ciphers; here we present a technique to construct Substitution-boxes by using linear recurrence relation to comply with the standards of good quality S-boxes. We have witnessed that the latest research relies more on improving already existing techniques, rather than developing wholly new methods. We use linear recurrence in an entirely new way. Real initial and obtained values are concealed by converting it into new numbers to avoid any pattern to follow. The obtained S-boxes are analyzed through performance tests to check the strength and quality of our S-boxes. Later we will encrypt an image and also perform encryption and decryption in noise channels to make it more applicable in low profile applications.