Though conjugate gradient methods are easy to be implemented in a computer for solving an unconstrained optimization problem, it is difficult to establish the theory of global convergence. To overcome this difficulty,a new conjugate gradient algorithm was investigated. In this algorithm, the search direction is constructed to be involved with three parameters, which are suitably chosen such that the obtained direction is always sufficiently descent one of the objective function, independent of any line search strategy. On basis of this direction, a nonmonotone conjugate gradient algorithm with three parameters is developed for solving unconstrained optimization problems. Under some mild assumptions, the global convergence theorem of this algorithm is proved. Preliminary numerical experiments demonstrate that the developed algorithm is more effective than the similar algorithms.