This paper proposes a utility-based resource allocation algorithm for the uplink OFDMA Inter-cell Interference (ICI) limited cooperative relay network. Full channel state information (CSI) is assumed to be available at the resource controller at initial stage, then the work is extended to consider more realistic assumption, i.e., only partial channel state information (PCSI) is available. The proposed algorithm aims to maximize the total system utility while simultaneously satisfying the individual user's minimum data rate requirements. In the proposed algorithm, relay selection is initially performed based on the consideration of ICI. Then, subcarrier allocation is performed to achieve maximum utility assuming equal power allocation. Finally, based on the amount of ICI, a modified water-filling power distribution algorithm is proposed and used to optimize the per-carrier power allocation across the allocated set of subcarriers. The results show that, compared to conventional algorithms, the proposed algorithm significantly improves system performance in terms of total sum data rate, outage probability and fairness.