In modern taxi networks, large amounts of taxi occupancy status and location data are collected from networked in-vehicle sensors in real- time. They provide knowledge of system models on passenger demand and mobility patterns for efficient taxi dispatch and coordination strategies. Such approaches face a new challenge: how to deal with uncertainties of predicted customer demand while fulfilling the system's performance requirements, including minimizing taxis' total idle mileage and maintaining service fairness across the whole city. To address this problem, we develop a data- driven robust taxi dispatch framework to consider spatial-temporally correlated demand uncertainties. The robust optimization problem has an objective function that is concave in the uncertain demand and convex in the decision variables, and constraints that are convex in the decision variables according to the practical requirements. We design a data-driven algorithm for constructing uncertainty sets of random demand vectors that provide a probabilistic guarantee for the performance of robust taxi dispatch solutions. It guarantees that the probability that the actual dispatch cost under the true demand vector being smaller than the optimal cost of the robust dispatch solutions with the uncertainty sets is greater than a desired probability value. We prove equivalent computationally tractable forms of the robust dispatch problem with the constructed closed convex polytope and second order cone types of uncertainty sets, using the minimax theorem and strong duality. Evaluations on four years of taxi trip data for New York City show that the probabilistic guarantee is satisfied. By selecting a probabilistic guarantee level that does not sacrifice the average cost much, the average demand- supply ratio error is reduced by 31.7%, and the average total idle driving distance is reduced by 10.13% compared with non-robust dispatch solutions.