Cellular internet-of-things (CIoT) systems are recently developed by the third-generation partnership project (3GPP) to support internet-of-things (IoT) services over the conventional mobile-communication infrastructures. The CIoT systems allow a large number of IoT devices to be connected through the random-access procedure, but the concurrent accesses of the massive devices make this procedure heavily competitive. In this article, we present an effective time-division random-access scheme built upon the coverage levels (CLs), where each CIoT device is assigned a CL and categorized based on its radio-channel quality. In our scheme, the random-access loads of device groups having different CLs are distributed into different time periods, which greatly relaxes instantaneous contention and improves random-access performance. To assess the performance of our scheme, we also introduce a mathematical model that expresses and analyzes the states and behaviors of CIoT devices using the Markov chain. Mathematical analysis and simulation results show that our scheme significantly outperforms the conventional scheme (without time-division control) in terms of collision probability, succeeding access rate, and access-blocking probability.