Abstract: In this paper, numerical simulation results of nonlinear Plasmoid instabilities are presented. A two dimensional incompressible MHD code is used to calculate the results. The adaptive mesh refinement and MPI techniques are enable in this code. Harris sheets are used as the initial equilibrium conditions and small perturbations of the current density are applied to make the system unstable. Sequences of plasmoid instability processses for different Lundquist numbers have been studied. The Harris sheets will always evolve in to thinner Sweet-In this paper, numerical simulation results of nonlinear Plasmoid instabilities are presented. A two dimensional incompressible MHD code is used to calculate the results. The adaptive mesh refinement and MPI techniques are enable in this code. Harris sheets are used as the initial equilibrium conditions and small perturbations of the current density are applied to make the system unstable. Sequences of plasmoid instability processses for different Lundquist numbers have been studied. The Harris sheets will always evolve in to thinner Sweet-Parker current sheets with shearing flows in the early stage. As the Lundquist number S ≥ 10⁵, the Sweet-Parker thin current sheets are unstable and secondary islands appear. The critical aspect ratio for the unstable Sweet-Parker thin current sheet is around 65. The larger the Lundquist number is, the thinner the Sweet-Parker sheet, and the more secondary islands appear. These secondary islands are ejected out along the current sheet, grow bigger with time and coalesce with each other in the later stage. The reconnection rate of the current sheet has been increased a lot due to secondary instabilities. The peak reconnection rates in each reconnection processes for different Lundquist number are picked about to study the relationship between the Lundquist number and the reconnection rate, which has been found no longer scales with Lundquist number as S^{- 1/2}, but weakly depends on S.