In this article, an event-triggered control with periodic time-varying parameters is designed to stabilize a class of periodic systems with exogenous disturbances in a network environment. The continuous-time periodic system is approximated by some linear subsystems with finite-number constant matrices based on a piecewise method. It can thus reduce the complexity of theoretical analysis. To tackle the reduction of unnecessary data transmission between the sensor (or controller) and the controller (or actuator), new event-triggering mechanisms are designed via output feedback. Special parameters are designed to eliminate Zeno behavior, and the minimum triggering interval is obtained according to the designed condition. Then, an event-triggered periodic piecewise system is modeled as an impulsive periodic piecewise system. The bounded stability, as well as the (Formula presented.) performance of the impulsive periodic piecewise system, are analyzed. Furthermore, the gains of the event-triggered controller are obtained by a method of variable substitution. Finally, the validity of the proposed control is demonstrated by an application example.