<p>The conjugate gradient method is one of the most effective algorithm for unconstrained nonlinear optimization problems. This is due to the fact that it does not need a lot of storage memory and its simple structure properties, which motivate us to propose a new hybrid conjugate gradient method through a convex combination of the Dai-Yuan algorithm, Hestenes-Stiefel algorithm, and Liu–Storey algorithm. Under certain conditions, the proposed methods guarantee a sufficient descent at each iteration and exhibit global convergence properties. Furthermore, numerical results demonstrate that the hybrid computational scheme based on the conjugacy condition is efficient and performs favorably compared to some well-known algorithms.</p>