Non-shear flow can change the O-point position of a magnetic island, and thus it may play an important role in the effects of resonant magnetic perturbation (RMP) on the single tearing mode. We employ the nonlinear magnetohydrodynamics model in a slab geometry to investigate how RMP affects the single tearing mode instability with non-shear flow. It is found that the driving and suppressing effects of RMP on single tearing mode instability will appear alternately. When the flow velocity is small, the suppressing effect plays a major role throug...