We study an initial-boundary-value problem of a nonlinear Korteweg-de
Vries equation posed on a finite interval $(0,2\pi).$ The whole system
has Dirichlet boundary condition at the left end-point, and both of
Dirichlet and Neumann homogeneous boundary conditions at the right
end-point. It is known that the origin is not asymptotically stable for
the linearized system around the origin. We prove that the origin is
(locally) asymptotically stable for the nonlinear system.