Abstract: We consider a constrained Markov Decision Problem (CMDP) where the goal of an agent is to maximize the expected discounted sum of rewards over an infinite horizon while ensuring that the expected discounted sum of costs exceeds a certain threshold. Building on the idea of momentum-based acceleration, we develop the Primal-Dual Accelerated Natural Policy Gradient (PD-ANPG) algorithm that guarantees an $\epsilon$ global optimality gap and $\epsilon$ constraint violation with $\mathcal{O}(\epsilon^{-3})$ sample complexity. This improves the state-of-the-art sample complexity in CMDP by a factor of $\mathcal{O}(\epsilon^{-1})$.