Abstract: The Mortar spectral element method and message passing interface(MPI) parallel computation technique have been used in studying turbulent mixing of Kelvin-Helmhtz instabilities, and the evolution mechanism of Kelvin-Helmhtz instabilities has been estimated with the calculation of momentum thickness, energy spectrum and total kinetic energy. The results show that, the three-dimensional Mortar spectral element method can effectively capture the turbulent mixing of Kelvin-Helmhtz instability, with cascading and combination of turbulent eddies clearly shown. In addition, the initial laminar fluid flow of Kelvin-Helmhtz instability gradually developed into a turbulent flow with continuous spectrum structure in the simulation, thus two-dimensional to three-dimensional transition can be achieved. The statistical turbulent kinetic energy reflects the viscous dissipation of the turbulent mixing. The validity of the spectral element code has been demonstrated, and the feasibility of the spectral element method in turbulent study has been proved.