In this paper we present a computationally efficient, suboptimal integer bit allocation algorithm that maximizes the overall data rate in multiuser orthogonal frequency division multiplexing (OFDM) systems implemented in wireless networks. Assuming the complete knowledge of a channel and allowing a subchannel to be simultaneously shared by multiple users we have solved this data rate maximization problem in two steps. The first step provides subchannel assignment to users considering the users' requests on quality of service (QoS) expressed as the minimum signal-to-noise ratio (SNR) on each subchannel. The second step provides transmit power and bit allocation to subchannels in order to maximize the overall data rate. To reduce computational complexity of the problem we propose a simple method which assigns subchannels to users and distributes power and bits among them. We have analyzed the performance of our proposed algorithm by simulation in a multiuser frequency selective fading environment for various signal-to-noise ratios and various numbers of users in the system. We have concluded that our algorithm, unlike other similar algorithms, is suitable for OFDM wireless networks, especially when signal-to-noise ratio in the channel is low. Also, the results have shown that the total data rate grows with the number of users in the system.