With the popularity of electric vehicles (EVs), the charging problem becomes more and more serious due to the lack of sufficient public charging facilities in many big cities. Especially, for the electric taxis (ETs) on an e-hailing platform, the relatively long waiting and charging time, compared to fuel vehicles, has nontrivial effects on drivers’ incomes and the whole service level of an e-hailing platform. Thus, it is significant to develop an efficient approach to arrange and coordinate the ET$\mathrm {s}'$ charging scheme. However, most previous studies focus on the coordination of personal EVs’ charging demands or operations aiming to reduce the charging costs of independent drivers and the load of the city’s power grid or maximize the profits of the charging stations. In this paper, we address the optimal charging problems of ETs to minimize the total out-of-service times of all ETs on an e-hailing platform. In particular, we formulate the problem as a mixed integer programming (MIP) model involving not only the optimal assignment between ETs and available charging piles but also the optimal charging sequence of ETs assigned to the same pile, based on the real-time charging demands of ETs and the statues of charging piles. The MIP model is efficiently solved by the art-of-state MIP resolver, Gurobi tool. A simulation experiment setting is established based on the real data from Didi e-hailing platform operating in Chengdu city, China. The computational results demonstrate that our MIP approach can observably reduce the total out-off-time of all ETs within acceptable computational time, comparing the existing approach in the literature, which apply first-come-first-service rule to determine the charging sequences of ETs.