Energy harvesting relay network is considered as the promising solution for a wireless communication network in our time. In this research, we present and demonstrate the system performance of the energy harvesting based two-way full-duplex relaying network over Nakagami-m fading environment. Firstly, we propose the analytical expressions of the achievable throughput and outage probability of the proposed system. In the second step, the effect of various system parameters on the system performance is presented and investigated. In the final step, the analytical results are also demonstrated by Monte-Carlo simulation. The numerical results demonstrated and convinced the analytical and the simulation results are agreed with each other.