The conjugate gradient (CG) method is one of an iterative method used to solve large-scale unconstrained optimization problems. This method is said to be efficient because it has global convergence properties and requires low memory. In this work, we present the global convergence analysis of the Malik-Mustafa-Sabariah-Sulaiman-Sukono-the second (MMSSS2) method under exact line search. By using some conditions, MMSSS2 method satisfies the sufficient descent condition and is also proven to be globally convergent. Finally, numerical experiments are presented to compare the computational performance of the MMSSS2 method with the other method. © 2024 American Institute of Physics Inc.. All rights reserved.