The small amplitude sloshing of ideal fluid in a partially fluid-filled cylindrical rigid tank with a rigid annular baffle was studied. Separating the complicated fluid domain into several simple subdomains, the velocity potential functions corresponding to every fluid subdomains were solved. By introducing the modal expansion method, the general expressions of the modal shapes functions of each subdomains were analytically deduced by using the method of separation of variables based on the superposition principle. According to the continuous conditions among the subdomain interfaces and the free fluid surface wave conditions, the velocity potential equations with unknown coefficients have been obtained. The unknown coefficients in the solutions and the natural sloshing frequencies were determined by using the Fourier series expansion and the Bessel series expansion. The convergence study shows the high accuracy. The numerical results were compared with those obtained by the Galerkin method based on the variational principle and those obtained by the finite element method. Excellent agreement has been achieved.