In this paper, a laser induced air plasma channel antenna (PCA) for high power microwave weapon is presented, and the dispersive characteristic for normal modes of PCA is analyzed. An approximate electromagnetic model of PCA is created. Starting from the wave equations for the longitudinal components in generalized cylindrical coordinate, the relations between the transverse components and the longitudinal ones of the electromagnetic fields are given. The strict characteristic equation of PCA is deduced by applying the boundary conditions of electromagnetic fields. In the limit cases, the results obtained in this paper are consistent with those given in the literature through comparison, which shows that the results of this paper are correct and effective. Finally, the dispersive curves of PCA are calculated, particularly the variations of their propagation properties with plasma parameters, channel radius and velocity of movement are discussed, which has set up a solid foundation for the development of the antenna.