Single-photon counting is a vital technique in the field of quantum optics. It is widely used in two-photon coincidence detection and correlation control. In this study, we employ a single-photon-counting card and a router to construct a three-photon coincidence system by using two-photon coincidence and time-division multiplexing. The software control is based on LabVIEW program. The system performs coincidence detection for two or three photons, provides real-time displays, and stores the results. We obtain good results when using the system to detect three beams of light generated via the six-wave mixing process. The system can be applied to classical light sources in the field of quantum communication and to other non-classical light sources with time-frequency quantum correlations produced via nonlinear processes.