The medium-voltage grid emulator is gaining popularity for testing grid-code compliance of large-capacity converters for renewable energy resources. The cascaded H-bridge converter based on active-front-ends is a promising candidate for high-power grid emulators owing to its high modularity and extendibility. However, the cascaded H-bridge topology-based grid emulator suffers the undesired and unpredictable large dc-link voltage ripple under output voltages with multiple-frequency components, e.g., when emulating the grid voltage flickers and harmonics. In this paper, the dc-link voltage ripple characteristics under multi-frequency output conditions are analyzed and a dc-link ripple suppression method adopting harmonic current injection is proposed. The injected current reference is generated by reconstructing the dc-link output current and added to the original active-front-end current control loop. Compared with the existing control methods, e.g., proportional-integral-resonant (PIR), the proposed method has a good voltage ripple suppression effect, especially for multi-frequency outputs. Furthermore, the proposed idea does not need complicated calculation or extra control loops and provides a feedforward reference for the current control, leading to a good dynamic response of dc-link voltage control. Finally, the performance of this suppression control scheme is verified on two 1200V@40kW power electronics building blocks of a cascaded H-bridge converter.