Abstract: High order accurate weighted essentially non-oscillatory(WENO) schemes are investigated and their applications of scalar conservation laws are discussed. The 1-D scalar conservation equation and 2-D scalar conservation equation are numerically calculate using the 5-th order WENO schemes for space discretization and the 3-th order TVD Runger-kutta method for time discretization,respectively. Numerical results show that the WENO schemes have high order accuracy and Essentially non-oscillatory