This paper is concerned with periodic dynamic event-triggered H1 control for networked switched linear systems with both mode-dependent average dwell time (MDADT) and asynchronous switching. Compared with the existing event-triggered results of the switched systems, a new type of event-triggered condition is proposed. By using the MDADT approach and multiple Lyapunov functions technique, sufficient conditions are proposed so that the closed-loop system is exponential stable with a weighted H1 performance. Furthermore, the corresponding criterion is proposed to design a set of controllers for the switched system with asynchronism. An example is provided to verify the superiority of the acquired results.