We have conducted high-fidelity large-eddy simulations on the separated flow around an airfoil with control by the DBD plasma actuator over a wide Reynolds number range. The Reynolds numbers based on a chord length were set to 63,000, 260,000 and 1,600,000. For the no control cases, the flow separates near the leading edge in laminar state at Reynolds numbers of 63,000 and 260,000, and massive turbulent separation occurs at Reynolds number of 1,600,000. The separation control with the burst actuation can achieve the flow reattachment through the promotion of the turbulent transition for the Reynolds numbers of 63,000 and 260,000, resulting in the improvement in both the lift and drag. On the other hand, the lift coefficient can be mainly increased over 45 % through the large-scale vortex paring induced by the burst plasma actuation for the Reynolds number of 1,600,000. The effects of the burst frequency on the separation control are evaluated based on the improvement of the aerodynamic performance. In this evaluation, the effective burst frequency non-dimensionalized by a chord length and freestream velocity (F+ = f+c=u∞) comes to change with the Reynolds number. While relatively high burst frequencies (F+ ≈ 5) show the good improvement in the lift-drag ratio at Reynolds number of 63,000, the lower burst frequency (F+ ≈ 1) shows the highest improvement at Reynolds number of 1,600,000. On the other hand, when the non-dimensional burst frequency based on the momentum thickness and edge velocity of the separation shear-layer (Fθs) is considered, the high liftdrag ratio can be recognized at Fθs ≈ 10-2 for all the Reynolds number conditions.