Abstract: In this paper, we propose a new algorithm for unconstrained optimization.It makes  Touati-Ahmed and Storey's  and Nocedal and Gilbert's hybrid conjugate gradient methods to be special cases under precise line search.From the construction of the new formula $\beta_{k}$, the   new algorithm satisfies descent  conditions turally. And this property depends neither on the line search used nor on the convexity of the objective function.Under normal conditions, we prove the new method  can ensure the global convergence. Numerical results also show its efficiency.