This paper aims to investigate the problem of event-triggered control for a networked system with two channels of random delays. First, a discrete-time event-triggered scheme, in which sensor information is only updated when it is necessary, is presented. Next, the system is modeled as a time-delay singular Markovian jump system with time-varying switching. Then, an event-triggered network-induced delay compensation strategy is proposed. Sufficient conditions guaranteeing the asymptotically stable are derived based on the Lyapunov-Krasovskii functional method together with the linear matrix inequality (LMI) technique. Finally, simulation results and a practical networked DC servo control system verify the effectiveness of the proposed strategy.