In the development of a theoretical description of the formation and stability of spontaneous cationic-anionic vesicles, one requires a rapid, yet reasonably accurate, computational method to calculate the electrostatic free energy, g(elec), of a charged vesicle. In turn, the evaluation of g(elec) via the charging process requires knowledge of the surface potentials of the charged vesicle. With this in mind, we derive approximate expressions for the outer and inner sui face potentials of a charged vesicle using the nonlinear Poisson-Boltzmann (PB) equation. The derivation is carried out in two stages; The first stage is based on a generalization of the dressed-ionic micelle theory to the case of charged vesicles. Specifically, the PB equation is utilized to estimate the potential gradients at the outer and inner surfaces of the vesicle, which are then substituted in the two boundary conditions that describe the variation of the electric field across the boundaries. Combined with an expression relating the inner surface potential to the center-point potential, a set of three algebraic equations is obtained. This set of equations can then be solved numerically to calculate the two surface potentials of the vesicle. In the second stage, by expanding around the surface potentials which correspond to a vesicle having an electrically neutral interior, the two surface potentials are expressed approximately in terms of the surface charge densities and other known vesicular characteristics such as the size of the vesicle. The resulting surface potentials can then be estimated directly and analytically without resorting to any numerical procedure. In general, the surface potentials obtained by using the equations derived in the two stages are found to agree well with those obtained by a direct numerical integration of the PB equation. The:approximate expressions for the vesicle surface potentials derived in this paper eliminate the need for a direct numerical integration of the PB equation, thus providing a much more efficient computational route. This in turn, greatly facilitates the evaluation of the electrostatic free energy of a charged vesicle via the charging process.