We introduce a novel variant of the recursive multilevel trust-region (RMTR) method, called MASTR. The method is designed for solving non-convex bound-constrained minimization problems, which arise from the finite element discretization of partial differential equations. MASTR utilizes an active-set strategy based on the truncated basis approach in order to preserve the variable bounds defined on the finest level by the coarser levels. This approach allows for fast convergence of the MASTR method, especially once the exact active-set is detected. The efficiency of the method is demonstrated by means of several numerical examples.