This paper proposes a Slotted ALOHA-Based cognitive radio (CR) network and investigates the throughput of both CR and overall network in the presence of Rayleigh fading. We consider a network that comprises of two different classes of users, primary users (PUs) and CR users. PUs are licensed users and access the channel at any time utilizing Time Division Multiple Access (TDMA) as a Medium Access Control (MAC) technique. CR users are non-licensed users and can access the channel by exploiting Slotted ALOHA as a random access scheme when it is not occupied by the PUs. This study has also revealed that the overall channel utilization can be improved by exploiting the spectrum holes without interfering with the PUs' transmissions.