To alleviate the range anxiety of drivers and time-consuming charging for electric buses (eBuses), opportunity fast-charging has gradually been utilized. Considering that eBuses have operational tasks, identifying an optimal charging scheduling will be needed. However, in the real world, arrival time and state of charge (SOC) of eBuses are uncertain. Therefore, it is challenging for the charging station to efficiently schedule charging tasks. To solve the problem, this paper develops a two-stage stochastic eBus charging scheduling model. In the first stage, eBuses are assigned to designated chargers. After the arrival time and SOC are realized, the second stage determines the charging sequence of eBuses on each charger. The objective is to minimize the penalty cost of tardiness by determining the charging start time and the corresponding charging duration time. Then, a sample average approximation (SAA) algorithm is applied. Additional numerical experiments are performed to verify the efficiency of the stochastic programming model and algorithm.