In this paper we focus on the subcarrier allocation for the uplink OFDMA based cooperative relay networks. Multiple cells were considered, each composed of a single base station (destination), multiple amplify and forward (AF) relay stations and multiple subscriber stations (sources). The effects of inter-cell interference (ICI) have been considered to optimize the subcarrier allocation with low complexity. The optimization problem aims to maximize the sum rate of all sources and at the same time maintain the fairness among them. Full channel state information (CSI) is assumed to be available at the base station. In the proposed algorithm the subcarrier allocation is performed in three steps; firstly the subcarriers are allocated to the Relay Stations (RSs) by which the received ICI on each RS is minimized. Then, the pre-allocated subcarriers are allocated to subscribers to achieve their individual rate requirements. Finally the remaining subcarriers are allocated to subscribers with the best channel condition to maximize the total sum of their data rates. The results show that the proposed algorithm significantly reduces the complexity with almost the same achievable rate of the optimal allocation in a single cell case. In case of multi-cell, the proposed algorithm outperforms the conventional algorithm in terms of total network achievable data rate and overall network complexity.