This article presents numerical solutions of the periodic time-dependent Ginzburg-Landau model for the type-Ⅱsuperconductors by a finite-difference approximation. Both the static and dynamical properties of a single vortex are studied as the exteal magnetic field varies. Vortex and anti-vortex can coexist and annihilate with time in the case of no exteal magnetic field, while the vortex will approach a steady state in the presence of magnetic field. We also study vortex dynamical behaviours while pinning centres exist in the sample and find that the pinning site, which has a significant potential to keep the vortex from moving, may trap the vortex.