In this study, the authors consider a delay control problem with proportional fair scheduling in time-varying wireless channels. For proportional fairness of transmission rates among users, a congestion control scheme is proposed for guaranteeing both throughput and delay of the wireless network. Specifically, a scheduling weight is introduced to control queue lengths without degrading the throughput of the network because the delay of users depends on their queue length. Using the asymptotic approximation technique, the throughput and delay performance of the proposed scheme are analysed and showed the multiuser diversity effect analytically in the Rayleigh-fading wireless channels. Finally, simulation results show that the proposed scheme improves delay without degrading throughput.