Over the past decade, wireless communications has experienced tremendous growth, and this growth is likely to multiply in the near future. The proliferation of mobile users and an ever increasing demand for multimedia services has resulted in greater capacity requirements. Radio frequency spectrum is scarce and cannot meet this ever increasing demand and the required Quality of Service (QoS) will no longer be achieved if efficient Radio Resource Management (RRM) solutions are not found. Conventional Radio Access Networks (RAN) have standalone Base Stations (BS) with capacity preconfigured for peak loads. These RANs have high call blocking and dropping rates since BSs resources cannot be shared. Cloud based RANs (C-RAN) have been proposed as a cost and energy efficient way of meeting high capacity demand of future wireless access networks by consolidating BSs to the cloud. Instead of relying on rejection of new call requests due to limited BS resources, C-RAN takes benefit of the cloud elasticity, which allows dynamic provisioning of cloud BS resources. This paper presents a novel C-RAN Call Admission Control (C-RAN CAC) to ensure Grade of Service (GoS) by improving blocking probability and improvement of call waiting times. Call blocking probability, call average waiting time and system utilization are used to evaluate the performance of the proposed CAC algorithm.