In this paper, we present a new adaptive trust-region method for solving nonlinear unconstrained optimization problems. More precisely, a trust-region radius based on a nonmonotone technique uses an approximation of Hessian which is adaptively chosen. We produce a suitable trust-region radius; preserve the global convergence under classical assumptions to the first-order critical points; improve the practical performance of the new algorithm compared to other exiting variants.Moreover, the quadratic convergence rate is established under suitable conditions. Computational results on the CUTEst test collection of unconstrained problems are presented to show the effectiveness of the proposed algorithm compared with some exiting methods.