To develop kinetics calculational capability of the analytic function expansion nodal methodology for space-dependent feedback problems, a novel method with the time-dependent solution decomposed into an analytic part and a polynomial correction part is proposed. The analytic part consists of the analytic solutions of the "quasi-static" diffusion equation and the polynomial part is determined by applying a Galerkin scheme. The results tested on several benchmark problems (two-dimensional and three-dimensional) show that 1 node/assembly calculation and a large time-step size can be used for high accuracy. The new feedback calculation method removes almost all the errors induced from space-dependent feedback. Also, it is shown that the coarse group rebalance acceleration scheme and conventional techniques for kinetics calculation (exponential transformation for time variable and bilinear weighting for control rod cusping problem) can be easily incorporated into the method.