A model of grain boundary (GB) diffusion along an isolated moving GB is proposed based on the Fisher model. The GB is assumed to move with a constant velocity v. Analytical solutions of the model are obtained, and methods of GB diffusion parameters determination in different experimental conditions are discussed. Application of conventional methods, like the 6/5-method, to moving GBs results in essentially (by a factor of about underestimated values of the product D'[delta]. For more correct estimation of D'[delta], the proposed exponential solution should be used in such cases. A detailed classification of kinetic regimes in a bicrystal, containing stationary and moving GBs, is introduced. A kinetic diagram, useful in designing GB diffusion experiments, is proposed.