A coupled-mode-theory-based approach is applied for the first time to model the recently developed coaxial cable Bragg grating (CCBG). Coupled wave equations are derived to correlate the geometrical discontinues associated with the CCBG structure with the energy coupling that occurs between the forward and backward propagating waves along the CCBG. This paper provides a novel approach to model the coupling coefficient that results in a simplified form of the coupled wave equations. The finite-difference method is used to solve the coupled wave equations numerically. Further, based on the dielectric distortion assumption, the closed-form solution of the CCBG problem has been given. The reflection and transmission spectra of a CCBG sample are calculated numerically and analytically, and are validated by 3-D full-wave electromagnetic simulations, as well as experimental results.