Abstract An immersed-boundary numerical method is applied to simulate the wake downstream of a two-dimensional heaving airfoil. A switch of vortex pattern is found to be the major reason that a deflected asymmetric wake reverses its deflection angle. Parameters of the heaving airfoil and flow that influence the onset and location of the vortex switching are discussed. While the previous literature deliberately discussed the wake deflection in the near wake region, this study shows that the deflection angle can change from the near wake to far wake regions. A cross-flow effective phase velocity is introduced to analyze the already-formed asymmetric wake behind the airfoil. A vortex dipole model and the related vortex dynamics analysis are developed to show that the change of the distance between the vortices is the primary factor that leads to the vortex pattern switching in the far wake.