The onset of thermal convection of a fluid confined completely in a finite vertical cylinder with internal heat sourer is examined by using the linear stability analysis. The Galerkin method is applied to solve the perturbation equations. The stability criteria for various aspect ratios are determined in terms of the Rayleigh number and a nondimensional parameter relative to the heat source. The effects of the aspect ratio and the sidewall thermal boundary conditions on the stability as well as the structure of the convective roll are investigated. In the limiting cases, the results compare well with the literature.