The flow over a supercritical airfoil in the transonic regime contains a lot of complex physical phenomena and interactions. High demands are made on the numerical model for an accurate numerical investigation of such a flow type. High-order (N ≥ 5) WENO (Weighted Essentially Nonoscillatory) schemes are appropriate for the numerical simulation of transonic flows, as they have the capability to capture shocks, resolve vortices, and predict their interactions. A high-order finite difference WENO scheme is applied to simulate the unsteady flow over the supercritical BAC3-11 [1] airfoil. The numerical results are compared with experiments carried out in a transonic shock tube and found in good agreement with the experimental data. The influences of Ma and Re number are studied.