Visible light communication (VLC) is considered an effective complementary solution for indoor wireless communication to achieve high-speed and secure data transmission. In the random access process of VLC, the collision problem caused by hidden terminals is prominent. The multiple packet reception (MPR) technique can effectively mitigate the multi-terminal collision in VLC and improve the performance and reliability of the system. We proposed, considering the MPR-capable uplink VLC system, a quality of service (QoS)-constrained admission control scheme based on the improved coati optimization algorithm (COA) to guarantee delay requirement. First, we adopt the ALOHA mechanism as the basis of the service, and the arrival stream consists of a primary arrival stream and a background arrival stream. Then, we evaluate the delay performance using the large deviation theory, and the optimization problem with the objective of maximizing the arrival rate is constructed. Finally, we incorporate a cat chaotic map, Lévy flight strategy, and t-distribution mutation strategy to improve COA, which makes solving the optimization problem more efficient. Simulation results show that the proposed algorithm is dependable and can improve the system resource utilization.