The ubiquitous nature of the Internet of Things (IoT) constitutes a set of stringent quality of service (QoS) requirements from the underlying 5G network. To address the issues, this paper proposes an enhancement for the channel access period (CAP) of the widely used IEEE 802.15.3C (millimeter wave (mmW)) standard using a priority mechanism that fulfills the requirement of prioritized channel access for the IoT based applications. According to the hybrid medium access control (MAC) protocol of the IEEE 802.15.3C, to reserve time-division multiple access (TDMA) based slot in channel time allocation period (CTAP), a node will first send a channel time allocation (CTA) request to piconet controller (PNC) by using carrier-sense multiple access with collision avoidance (CSMA/CA) mechanism in the contention-access period (CAP). After successful delivery of CTA’s request, PNC will reserve a CTA for a specific node. However, there is no guarantee that a node will get a channel in the contention process in the existing standard. Hence, the existing CAP mechanism could demonstrate a bottleneck for a data sending device in terms of less delay and high throughput. To solve this issue, we first design a numerical model of CAP using the IEEE 802.15.3C standard’s specification, and then we propose a priority-based mechanism with three priority classes: high priority (HP), medium priority (MP), and low priority (LP) with each class having different contention windows (CW) range that makes the value of backoff period shorter. To evaluate the performance of the proposed mechanism, modifications are applied to the proposed numerical model. The performance comparison is conducted among prioritized classes devices in terms of transmission delay, channel access delay, and throughput. The conducted evaluations include two types of data rates i.e., 1.5 Gbps and 3 Gbps. The proposed scheme shows promising results for a node that requires high priority in an IoT environment.