In a massive machine-type communication (MTC) environment, a traffic control algorithm is essential to solving traffic congestion problems. Additionally, as MTC applications have diverse quality-of-service requirements, traffic control should be applied in a way that guarantees diverse requirements. Therefore, we propose a priority-based access class barring (PACB) scheme, in which MTC devices are divided into multiple classes according to their delay requirements, and a different access class barring (ACB) factor is used for each class. This article suggests an approach to choose multiple ACB factors that can maximize the number of successful access events and can also guarantee the low delay requirement of the high-priority class. Then, an analytical model is proposed for the ideal case, and throughput, drop probability, and access delay are derived to evaluate the performance. For a realistic environment, we also suggest an estimation algorithm for the PACB scheme, in which a base station estimates the number of active devices for each class. Numerical and simulation results showed that the analytical model is consistent with the simulation results. Additionally, the performance of the estimation algorithm was similar to that of the ideal case. Furthermore, the proposed PACB scheme can decrease the delay of a high-priority class and improve the throughput and drop probability compared to existing algorithms.