A fence structure includes a plurality of vertical pickets, at least one connecting strip, a plurality of pivot members, and at least one transverse railing. One end of the pivot member is provided with a stop portion whose outer diameter is larger than the inner diameter of the pivot hole of the vertical picket. The stop portion may limit the pivot member and prevent the pivot member from slipping axially after passing through the connecting strip and the vertical picket. By the aforesaid arrangement, the pivot member not only allows the angle of the transverse railing and the connecting strip to be adjustable according to needs, but also prevents the connecting strip and the vertical pickets from slipping or disconnecting resulting when being exerted by a pulling or pushing force.