Abstract: An initial-boundary value problem of the Korteweg-de Vries equation is considered. A conservation law fox this problem is derived. A difference scheme is introduced and its conservation property is compared to the conservation law. The convergence of this scheme is strictly proved. It is shown numerically that such scheme is applicable. Numerical results for the case where the initial condition is zero and the boundary condition is a rectangle pulse are also obtained. It is found that the solution exhibits soliton-like behaviour.