In this paper, resource allocation for OFDMA system with proportional rate constraints is studied. The objective is to optimize subcarriers and power allocation in order to maximize sum capacity subject to the constraints of total power and proportionality among users' capacity. Optimal solution to the constrained fairness maximization problem is extremely computationally expensive. Previous works have proposed suboptimal solution by separating the subcarrier and channel allocation. Although previous work offered a suboptimal solution which is 95% close to the optimal but the resource allocation algorithm is found biased to the users which suffer deep fading and can only work in high channel-to-noise ratio condition. We propose a resource allocation algorithm to overcome these issues. The numerical results show that the proposed algorithm consistently yields higher sum capacity and better fairness in resource allocation among users.