We study distributionally robust optimization (DRO) problems where the ambiguity set is dened using the Wasserstein metric. We show that this class of DRO problems can be reformulated as semi-innite programs. We give an exchange method to solve the reformulated problem for the general nonlinear model, and a central cutting-surface method for the convex case, assuming that we have a separation oracle. We used a distributionally robust generalization of the logistic regression model to test our algorithm. Numerical experiments on the distributionally robust logistic regression models show that the number of oracle calls are typically 20~50 to achieve 5-digit precision. The solution found by the model is generally better in its ability to predict with a smaller standard error.