An analytical model was proposed in this paper to predict the burst pressure of a pipe with geometric eccentricity. With application of the complex elastic potential function method in a bipolar coordinate system, the authors first derived an analytical solution of stresses in an eccentric pipe and then obtained the formula of predicting burst pressure by combining the solution with the Tresca criterion. Finally, the effect of eccentricity and the ratio of thickness to diameter of pipe on burst pressure were discussed. Our results show that a slight eccentricity can significantly decrease the burst pressure. In the special case of zero-eccentricity for a concentric pipe, our model yields results that are consistent with experiments data published by others and theoretical results predicted by models proposed by other researchers without considering the effect of eccentricity. In the case of eccentricity for an eccentric pipe, the calculating results of our model are also consistent with that of finite element model (FEM). The theoretical model and results presented in this paper have a broader application in predicting the burst pressure for pipes commonly used in oil and gas industry.