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 magnetohydrody-namics 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 alteately. When the flow velocity is small, the suppressing effect plays a major role through the development of the mode, and the tearing mode instability will be suppressed. With the flow velocity increasing, the driving effect will increase, while the suppressing effect will decrease. When the two effects reach equilibrium, the tearing mode will become stable.