A numerical scheme to construct a two-way, movable, nested-mesh primitive equation model is proposed. Dynamical coupling in a two-way nesting system is performed at a dynamical interface which is separated from a mesh interface by two coarse-grid intervals. Dynamical interaction is achieved by a method which conserves mass, momentum and internal energy of the system. During the course 'Of integration, the nested mesh moves so that the central position of the disturbance contained in The fine-mesh area never deviates from the center of the nest by more than one coarse-mesh interval. New grid data near the leading and trailing edges of the moving nest are obtained by an interpolation method which has a conservation property. The proposed methods of dynamical coupling and mesh movement were extensively tested by a one-dimensional shallow water equation model. Numerical results of these experiments are presented.