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Abstract The features of magnetic reconnection with a streaming flow have been investigated on the basis of compressible resistive magnetohydrodynamic (MHD) model. The super-Alfvenic streaming flow largely enhances magnetic reconnection. The maximum reconnection rate is almost four times larger with super-Alfvenic streaming flow than sub-Alfvénic streaming flow. In the nonlinear stage, it is found that there is a pair of shocks observed in the inflow region, which are manifested to be slow shocks for sub-Alfvénic streaming flow, and fast shocks for super-Alfvénic streaming flow. The quasi-period oscillation of reconnection rates in the decaying phase for super-Alfvénic streaming flow is resulted from the different drifting velocities of the shock and the X point.