Trust region method for a class of large-scale minimization problems, the unconstrained discrete-time optimal control (DTOC) problems, is considered. Although the trust region algorithms developed in [4] and [13] are very economical they lack the ability to handle the so-called hard case. In this paper, we show that the trust region subproblem can be solved within an acceptable accuracy without forming the Hessian explicitly. The new approach is based on the inverse power method for eigenvalue problem and possesses the ability to handle the hard case. Our proposed approach leads to more efficient algorithms for DTOC problems.