We have studied the effect of local surface potential distribution on its relaxation in the polycrystalline ferroelectric thin films. A lower surface potential region, i.e., potential pit, is generated near a grain boundary. The deep potential pit has a faster relaxation than the area far away from the potential pit due to the acceleration of the screen charge draining near the grain boundary and the domains formed by applying higher voltage have a faster relaxation due to the larger gradient of screen charge distribution. In addition, the surface potential and its relaxation depend on the sign of applying voltage. The result shows that the surface potential distribution may influence significantly to the reliability of bit signal on the memory devices.