A new hybrid conjugate gradient algorithm is considered. The conjugate gradient parameter $\beta_k$ is computed as a convex combination of $\beta_k^{CD}$ and $\beta_k^{LS}$. The parameter $\theta_k$ is computed in such a way that the conjugacy condition is satisfied. The strong Wolfe line search conditions are used. Numerical comparisons show that the present hybrid conjugate gradient algorithm often behaves better than some known algorithms.