The analysis of the three-dimensional continuous refueling is approximated by the variational method. The axial flux distribution is treated by the trial function and expressed by the analytic expression, using the elliptic function. Introducing the perturbation technique in the flux expansion, the higher order cross-section expansion correction of the axial flux distribution is achieved by using the elliptic function as the base function in the flux expansion. It is shown that the group constants, averaged by the flux and its square, can be expressed by the simple rational function. As a special example, the nature of the eigenvalue under continuous unidirectional refueling is shown, and it is pointed out that some caution is required if the fuel burnup is evaluated by the reactivity-area method.