 The steepest descent method and the conjugate gradient method to minimize non-linear functions have been studied in this work. Algorithms are presented and implemented in MATLAB software for both methods. However, a comparison has been made between the steepest descent method and the conjugate gradient method. The obtained results in MATLAB software has time and efficiency aspects. It is shown that the conjugate gradient method needs fewer iterations and has more efficiency than the steepest descent method. On the other hand, the steepest descent method converges a function in less time than the conjugate gradient method. This article was authored by Dana Taha Muhammad Saleh and Bawar Muhammad Faraj.