In this paper, a novel distributed power control (DPC) scheme for cellular network in the presence of radio channel uncertainties such as path loss, shadowing, and Rayleigh fading is presented. Since these uncertainties can attenuate the received signal strength and can cause variations in the received Signal-to-Interference ratio (SIR), a new DPC scheme, which can estimate the slowly varying channel uncertainty, is proposed so that a target SIR at the receiver can be maintained. Further, the standard assumption of a constant interference during a link's power update used in other works in the literature is relaxed. A CDMA-based cellular network environment has been developed to compare the proposed scheme with earlier approaches. The results show that our DPC scheme can converge faster than others by adapting to the channel variations. In the presence of channel uncertainties, our DPC scheme renders lower outage probability while consuming significantly low power per active mobile user compared with other schemes that are available in the literature.