Cloud-based radio access networks (C-RANs) are an emerging technology for 5G cellular networks. The increasing demand for radio resources causes many challenges in managing resources, such as power and interference management, user association, and spectrum allocation. This study aims to handle resource allocation challenges. We propose a novel model to maximize channel utilization by employing an auction mechanism applied in the C-RAN framework. We provide an unit-based allocation considering users’ maximum and minimum demands. We expect that the proposed schema will increase auctioneer revenue, maximize channel utilization, and maximize user satisfaction while meeting users’ demands. Moreover, we conduct a comparison between the proposed schema and the previous standard method. The results of the comparison show that the proposed scenarios increased the spectrum utilization by 66%, maximized revenue by 166%, increased the user satisfaction by 22%, and increased Jain’s fairness index by 17%. Consequently, these outcomes prove the effectiveness of the proposed method. A plan to find the optimal values for simulation parameters to get better results by applying a different winner determination problem (WDP) strategy is considered as future work.