Superconductivity is a phenomenon that manifests quantum physics on a macroscopic scale. Its applications are diverse and currently maintains an active research field, for example, the search for high temperature superconductors and the technological implementation of type II superconductors whose configuration of vortices can even be observed in superfluids or in Bose-Einstein condensates. In particular, in this work a two-dimensional type II mesoscopic superconductor is simulated using the Ginzburg-Landau theory and the finite difference method, in order to observe how the vortices behave, their vorticity and the magnetization curves work in systems of mesoscopic dimensions.