A new suction-blowing joint control technique is developed to reduce airfoil drag. The technique realizes suction at the airfoil leading edge and blowing at the trailing edge. As key to the difficulty of transition control, the accuracy of transition prediction under suction control is assessed by comparing the computational results with the data of a reliable experiment, and the solutions show that the corrected Wilcox transition model most accurately predicts the transition position induced by the suction. Many numerical simulations are then conducted over a range of parameters (slot width, spacing, etc.) for suction-blowing control. The physical mechanisms that govern suction and blowing drag-reduction control are determined and analyzed, and the impacts of the air mass flow rate through the slots, slot width, spacing, and size of porous region on the drag-reduction effect are discussed. Additionally, the numerical results show that suction-blowing control results in a lower drag compared with suction without blowing. The current numerical studies create a useful knowledge base for further exploration of 3-D wing suction-blowing control design.