Start-time of magnetic reconnection under typical interplanetary parameters has been numerically simulated by using the two-dimensional compressible magnetohydrodynamic equations with a third-order compact upwind scheme. Magnetic reconnection would occur near the interplanetary current sheet impacted by a plasmoid.Its initiation is associated with the interplanetary plasma parameter β and the momentum of the plasmoid.The higher the β value is, the faster the reconnection takes place. Meanwhile the reconnection occurs earlier with increasing the plasmoid momentum, and increasing driving velocity is more effective in initializing the reconnection than that of the plasma density when the other factors are kept to be the same. The evolution of the reconnection with the heliocentric distance is also investigated.