The emergence of optical wireless networks (OWNs) is a potential solution to the quest for the increasing bandwidth demand. Existing bandwidth assignment strategies are not suitable for OWNs, considering factors such as differences between the physical properties of radio networks and OWNs. In order to eliminate collision, minimize delay and enhance system utilization and fairness, we propose the non-contention bandwidth assignment protocol called adaptive polling medium access control (APMAC) protocol for OWNs. The APMAC protocol involves association, data transmission and dissociation phases. Moreover, the APMAC protocol exploits features of the IEEE 802.15.7 visible light communication (VLC) standard. While assigning bandwidth to the visible light nodes (VLNs), the visible light access point (VLAP) establishes a polling table that contains the identity, buffer size and round-trip time of each VLN that issued bandwidth request. The contents of the polling table enable the computation of the maximum transmission unit and time-slot for each VLN that requests bandwidth assignment. In order to achieve convincing results, we simulate the protocol under varying network sizes ranging from 1 to 10 VLNs per access point, then we compare the results against the medium transparent medium access control (MT-MAC) protocol that is a non-contention MAC protocol. We demonstrate numerical results of our study considering average waiting time, packet collision, system utilization and fairness. Numerical results reveal that the APMAC protocol outperforms the MT-MAC protocol.