We conduct large-eddy simulations of separated airfoil flows with control by a dielectric-barrier-discharge plasma actuator over a wide range of Reynolds numbers. The Reynolds numbers based on the chord length (Re) are set at Re = 5.0 × 103, 1.0 × 104, 6.3 × 104, 2.6 × 105, and 1.6 × 106. These Reynolds numbers cover most of the conditions used in the previous studies on separation control by a plasma actuator. The burst frequency nondimensionalized by the chord length and freestream velocity (F+) is used as the computational parameter, and the effective burst actuation and control mechanisms at each Reynolds number condition are investigated. With regard to cases without the control, the flows separate near the leading edge in the laminar state at the Reynolds number range of 103-105, and a substantial turbulent separation occurs at the Reynolds number of 1.6 × 106. Separation control with a high burst frequency [F+ ≃ O(10)] can cause early flow reattachment through the promotion of turbulent transition of a separation shear-layer for Re = 6.3 × 104 and 2.6 × 105. Flow reattachment is mainly caused by momentum entrainment into the boundary layer by fine-scale turbulent vortices. On the other hand, the large-scale spanwise vortices play an important role at F+ = 1 for Re = 1.0 × 104 and 1.6 × 106. In these cases, the dynamics of the spanwise vortices show similar behavior and the pairing of these vortices significantly contributes to the separation control by increasing the momentum entrainment. The optimum value of F+ changes with a Reynolds number. In contrast, when a nondimensional burst frequency based on the characteristics of the separation shear-layer (Fθs) is considered, a high lift-to-drag ratio is found at Fθs≃O(10-2) for all Reynolds numbers. This demonstrates that one of the effective burst frequencies is closely related to the scale of the separation shear-layer, especially for the spanwise vortex shed from the separation shear-layer.