There are various flow interactions between the fore- and hindwings of a dragonfly. However, the detailed mechanism of flow interaction between the fore- and hindwings has not been well understood. In this study, we clarify the aerodynamic mechanisms of flow interaction between fore- and hindwings of a dragonfly in hovering and forward flights. Measurements of unsteady aerodynamic forces acting on the tandem wings are conducted using a dynamically scaled mechanical model in a water tunnel. Moreover, flow visualization around the tandem wings is conducted using Particle Image Velocimetry. The effect of the phase difference between the fore- and hindwings on the aerodynamic characteristics is investigated in hovering and forward flights. The results indicate that the advanced hindwing ahead of the forewing, which is often used in steady flights of dragonflies, has a smaller variation with respect to the phase difference and a smaller difference between the fore- and hindwings in hovering and forward flight. In hovering flight, the flow interaction reduces the aerodynamic characteristics except at the phase difference of 0 deg. In forward flight, the advanced hindwing generates larger lift with a good efficiency than that without interaction.