The time-dependent numerical method is used to solve Navier-Stokes equations and simulate the 2D shockwave planar boundary-layer interaction. In our computation, the high order accuracy WENO schemes are applied to pursuing numerical approximation of the inviscid spatial derivative. To step on time, we make use of the Runge-Kutta methods with property of TVD. The viscous term is discremeted by two-order central difference scheme. The resultant pressure and shear distribution agree with those of the experiments. The numerical practice shows the WENO schemes are robust and strong indeed, and have a vast range of prospects for application.