We propose a suboptimal optimization algorithm for user maximization and resource allocation in an OFDMA based cognitive radio network. The aim is to admit as many secondary users as possible while satisfying quality of services for each admitted secondary user and ensuring the interference leakage to primary network is below a threshold. The original problem which is a combinatorial optimization problem becomes computationally prohibitive as the problem dimension in terms of the number of users seeking access to the network increases. However, our proposed suboptimal algorithm performs very closely to the optimal combinatorial optimization algorithm while keeping the complexity substantially low.