Abstract: Using the multistep implicit scheme,a numerical study was made to reveal the influence of linear force-free field to the spontaneous reconnection of current sheets.It is found that the background field (force-free field)of current sheets can strongly affect the topology of the reconnection.When the force-free factor a reaches a critical value,a big area of magnetic island forms in the simulation domain,and the thickness of the island is an increasing function of times.But if the force-free factor is smaller,than the critical value, no islands can be formed.When a is zero,it turns to the common single Xline reconnection of potential field.The reconnection topology of the potential field agrees to that of Scholar.