Recently, policy optimization for control purposes has received renewed\nattention due to the increasing interest in reinforcement learning. In this\npaper, we investigate the convergence of policy optimization for quadratic\ncontrol of Markovian jump linear systems (MJLS). First, we study the\noptimization landscape of direct policy optimization for MJLS, and, in\nparticular, show that despite the non-convexity of the resultant problem the\nunique stationary point is the global optimal solution. Next, we prove that the\nGauss-Newton method and the natural policy gradient method converge to the\noptimal state feedback controller for MJLS at a linear rate if initialized at a\ncontroller which stabilizes the closed-loop dynamics in the mean square sense.\nWe propose a novel Lyapunov argument to fix a key stability issue in the\nconvergence proof. Finally, we present a numerical example to support our\ntheory. Our work brings new insights for understanding the performance of\npolicy learning methods on controlling unknown MJLS.\n