Computations of transonic flows over a practical wing-fuselage geometry designed for a transonic transport aircraft are carried out using three-dimensional Reynolds-averaged “thin-layer” Navier-Stokes equations. The thin-layer approximation is extended to two directions to evaluate viscous layers on both the wing and fuselage surfaces. The LU-ADI factorization algorithm is used with the implementation of new smoothing terms. Computations are done for several angles of attack with the specified Mach and Reynolds numbers corresponding to the experiment, and the comparison of the computed surface pressure to the experimental data shows good agreement. The computed results reveal the effect of the fuselage near the wing root, especially at relatively high angles of attack. It is shown that the flow pattern when a fuselage exists is quite different from that for an isolated wing. This indicates the importance of the computation over a wing-fuselage combination using Navier-Stokes equations. The computations, which uses about 700,000 grid points, requires about 5-6 h of computer time on a Japanese supercomputer for each case.