Cognitive radio network is an intelligent and adaptive communication technology used to effectively utilize the radio spectrum to provide better communication. It enables the secondary (unlicensed) users to communicate over vacant channels without disrupting the communication of the primary (licensed) users. This paper proposes a novel contention-free MAC protocol for full-duplex and half-duplex cognitive radio networks. A novel concept of a fusion center-based channel allocation scheme is proposed to provide better channel allocation and reduced energy consumption. The proposed technique is compared with the existing techniques in terms of the average number of channels being sensed by each user, average wait time, collisions, throughput, and average energy consumption. The number of collisions increases as the maximum allotted time of communication increases in existing approaches. The experiment is performed with 20, 40, 60, and 80 s. The existing approaches show for 20 s, the number of collisions is 65, 61, 68, and 62; for 40 s, the number of collisions is 93, 96, 95, and 92; for 60 s, the number of collisions is 122, 126, 133, and 130; for 80 s, the number of collisions is 176, 170, 173, and 175. The proposed method approaches the number of collisions will become zero as the maximum allotted time of communication increases. The experimental results show that the proposed approach performs better than existing approaches. Moreover, it can be observed that the average waiting time of secondary users when a collision occurs is reduced with the application of a fusion center-based channel allocation scheme.