We propose a trust region method for policy optimization that employs Quasi-Newton approximation for the Hessian, called Quasi-Newton Trust Region Policy Optimization (QNTRPO). Gradient descent is the de facto algorithm for reinforcement learning tasks with continuous controls. The algorithm has achieved state-of-the-art performance when used in reinforcement learning across a wide range of tasks. However, the algorithm suffers from a number of drawbacks including: lack of stepsize selection criterion, and slow convergence. We investigate the use of a trust region method using dogleg step and a Quasi-Newton approximation for the Hessian for policy optimization. We demonstrate through numerical experiments over a wide range of challenging continuous control tasks that our particular choice is efcient in terms of number of samples and improves performance.