Conjugate gradient techniques are popular methods for solving large-scale nonlinear optimization problems. In this paper, we develop a new hybrid conjugate gradient algorithm. The proposed method is derived from a convex utilization of two well-known successful conjugate gradient algorithm conjugate gradient algorithms. The conjugacy property for the new method is preserved, in addition to the downhill direction property and global convergence, proven under the strong Wolfe linear search conditions. Numerical outcomes show that the new method is efficient and robust as it outperforms six of the popular conjugate gradient methods.