Federated reinforcement learning (FedRL) enables agents to collaboratively train a global policy without sharing their individual data. However, high communication overhead remains a critical bottleneck, particularly for natural policy gradient (NPG) methods, which are second-order. To address this issue, we propose the FedNPG-ADMM framework, which leverages the alternating direction method of multipliers (ADMM) to approximate global NPG directions efficiently. We theoretically demonstrate that using ADMM-based gradient updates reduces communication complexity from ${O}({d^{2}})$ to ${O}({d})$ at each iteration, where $d$ is the number of model parameters. Furthermore, we show that achieving an $ε$-error stationary convergence requires ${O}(\frac{1}{(1-γ)^{2}ε})$ iterations for discount factor $γ$, demonstrating that FedNPG-ADMM maintains the same convergence rate as the standard FedNPG. Through evaluation of the proposed algorithms in MuJoCo environments, we demonstrate that FedNPG-ADMM maintains the reward performance of standard FedNPG, and that its convergence rate improves when the number of federated agents increases.