A new homogenization scheme is suggested and investigated in order to solve the control rod cusping problem of nodal methods in light water reactor analysis. This cusping problem arises if a partially rodded node is represented by homogenized parameters of magnitude proportional to the volume of control rod material present, that is, by volume-weighting method, and may induce considerable error in transient calculations. The distinctive feature of the new method, named the flux-and adjoint flux-weighting method, is that in addition to forward flux adjoint flux is used as a weighting function in determining the homogenized cross sections of a partially rodded node, while only the forward flux shape is utilized in the traditional equivalence theory approaches. The motivation for using the adjoint flux as a weighting function is based on the fact that using the adjoint flux together with the forward flux can result in more accurate perediction of the homogenized cross sections, even though the forward flux shape is not accurate enough, since the adjoint flux at a position represents the relative importance of neutron at the position. In this method, the forward flux shape is approximated by polynomial expansions and the adjoint flux shape is obtained on the basis of the modified one-group theory. The new method is applied to two transient benchmark problems and is found to be more accurate than conventional methods including volume-weighting method and quadratic axial flux expansion method. Results obtained are compared with those of conventional methods. Use of the new method substantially reduces the errors caused by the control rod cusping problem. The flux-and adjoint flux-weighting method is shown to be simpl, but systematic, and problem-independent.