<p>In this paper, based on a combination of the retrospective idea and a non-monotone strategy, we propose a modified non-monotone adaptive retrospective trust region algorithm. Unlike traditional trust region algorithms, the trust region radius is updated adaptively based on the retrospective ratio. On the other hand, the proposed algorithm takes advantage of the line search and new non-monotone strategies to increase the probability of acceptance of the trial step. Theoretical analysis indicates that the new algorithm preserves the global convergence under classical assumptions. Moreover, superlinear and quadratic convergence are established under some standard conditions. Finally, the practical competencies of the algorithm are investigated by numerical experiments on a set of test functions. The results demonstrate its computational efficiency.</p>