This article presents an event-triggered distributed secondary control with predictive compensation based on the model-free predictive control under Denial-of-Service (DoS) attacks in ac/dc-networked microgrids. First, models of ac/dc networked microgrids in both electric network and communication network are established. On this premise, event-triggered distributed secondary control is proposed to solve the problems of strong communication burden and low-power distribution accuracy. Besides, aiming at the impact of DoS attacks on distributed secondary control, a compensation algorithm based on model-free predictive control is designed to estimate the control variables when the DoS attack occurs, which can improve the control performance and maintain the stable operation without a specific system structure system. Then, the convergence of event-triggered distributed secondary control with the condition of whether DoS attacks happen are analyzed. Finally, the effectiveness of the proposed control is verified on the hardware-in-loop (HIL) simulation platform consisting of the RT-LAB simulator, MATLAB/Simulink simulation model, and DSP controller.