The hybrid conjugate gradient methodsare combinations of different conjugate gradient (CG) algorithms to give better performance. This paper develops a new hybrid method of conjugate gradient type,satisfies the sufficient descent condition under the exact line search conditions and becomes globally convergent. Preliminary numerical experiments are tested on a set of unconstrained optimization test problems. The resultsof comparisons showthe computational efficiency of the developed hybrid method by solving selected large-scale benchmark test functions againstsome known algorithmsin the sense of Dolan–More performance profile.