This paper presents analysis of outage probability of an amplify-and-forward (AF) orthogonal frequency division multiplexing (OFDM) based relay network with maximal ratio combining (MRC) technique at the receiver. In this paper, a closed-form expression for a tight lower-bound of outage probability is derived under the frequency selective Nakagami-m fading channels, where m is an integer. A non-linear power amplifier (PA) is considered at the relay node which introduces the non-linear distortion. This analysis describes the effect of non-linear PA parameters over outage probability at various signal-to-noise ratio (SNR) levels. The numerical values of outage probability expression is compared with computer simulations to verify the accuracy of the derivation.