The characteristic-based time domain method, developed in the computational fluid dynamics community for solving the Euler equations, is applied to the antenna radiation problem. Based on the principle of the characteristic-based algorithm, a governing equation in the cylindrical coordinate system is formulated directly to facilitate the analysis of body-of-revolution antennas and also to achieve the exact Riemann problem. A finite difference scheme with second-order accuracy in both time and space is constructed from the eigenvalue and eigenvector analysis of the derived governing equation. Rigorous boundary conditions for all the field components are formulated to improve the accuracy of the characteristic-based finite difference scheme. Numerical results demonstrate the validity and accuracy of the proposed technique.