Abstract: The numerical solution for an initial boundary value problem of Rosenau - KdV equation is considered. A linear three-level conservation finite difference scheme with two weighted coefficient is designed. The finite difference scheme simulates the conservation properties of the problem well. The prior estimate, existence and uniqueness of the finite difference solution are also obtained. It is proved that the finite difference scheme is convergent with second-order and unconditionally stable with discrete functional analysis method. Numerical experiment result also shows that appropriate adjustments to the two weighted parameters would significantly improve the computational accuracy.