<p>In this study, we propose a trust region algorithm that inherits the remarkable properties of non-monotone strategy and adaptive radius. The radius of the algorithm is calculated based on a modified secant equation, using the values of the objective function and the gradient simultaneously in each iteration. The new non-monotone strategy is introduced to avoid the effect of monotonicity in slowing down the convergence speed, which leads to better practical and theoretical advantages than the previous non-monotone trust region algorithms. The global and superlinear convergence of the proposed algorithm are established under some standard conditions. Finally, the numerical experiments show the reduction of workload by the new algorithm and its efficiency.</p>