A fully implicit multiblock aeroelastic solver, which coupled thin-layer Navier-Stokes equations with structural equations of motion, has been developed for the flutter simulation on complex aerodynamic configurations. Navier-Stokes equations are solved with a lower-upper symmetric Gauss-Seidel subiteration algorithm and a modified Harten-Lax-van Leer-Einfeldt-Wada scheme. Structural equations of motion are discretized by a direct second-order differential method with subiteration in generalized coordinates. The transfinite interpolation is used for the grid deformation of the blocks neighboring the flexible surface. To evaluate the effectiveness of the grid deformation, a comparison is first done for the oscillating LANN wing with a rigidly attached grid and a deforming grid. Then the method is applied to predict the flutter speed and frequency of the AGARD 445.6 standard aeroelastic wing. Finally, the aeroelastic instability referred to as aileron buzz is simulated for the supersonic transport model of the National Aerospace Laboratory of Japan.