Abstract: In this paper, we propose a non-monotone adaptive trust region algorithm based on conic model for solving unconstrained optimization problems. Unlike the traditional non-monotone trust-region method, our proposed algorithm avoids resolving the sub-problem whenever a trial step is rejected. Instead, it performs a non-monotone Armijo-type line search in direction of the rejected trial step to construct a new point. The algorithm can be regarded as a combination of non-monotone, line search and conic trust region method. Theoretical analysis indicates that the new approach preserves the global convergence to the first-order critical points under classical assumptions.