Limited-memory quasi-Newton methods and trust-region methods represent two efficient approaches used for solving unconstrained optimization problems. A straightforward combination of them deteriorates the efficiency of the former approach, especially in the case of large-scale problems. For this reason, the limited memory methods are usually combined with a line-search. The trust region is usually determined by a fixed vector norm, typically, scaled $l_2$ or $l_{\infty}$ norms. We present a trust-region approach where the model function is based on a limited-memory quasi-Newton approximation of the Hessian, and the trust region is defined by a specially designed norm. Since this norm depends on certain properties of the Hessian approximation, the shape of the trust region changes with every iteration. This allows for efficiently solving the subproblem. We prove global convergence of our limited-memory methods with shape changing trust region. We also present results of numerical experiments that demonstrate the efficiency of our approach in the case of large-scale test problems.