Based on the 2nd order NND scheme, a third order WNND scheme was constructed with Jiang and Shu's weighted idea and third order TVD Runge-Kutta method.It was applied in solving linear equation,1D Euler equations and 3D Navier-Stokes equations. The numerical results indicate that WNND scheme brings about less dissipation and spurious oscillations,and it can catch the discontinuities of the flow field.