Electric vehicles (EVs) will become a component of the future generation intelligent transportation system. Because of EVs' limited battery power, the wireless power transfer (WPT) system has drawn much attention in recent years. The WPT system charges EVs in motion when they pass the charging lanes installed in roads without requiring physical contact between utility power supply and vehicle battery. A charging lane has limited power that can be transferred to EVs on the charging lane. A challenge here is how to allocate the limited power to the EVs so that they have sufficient power to arrive at the next charging lane or their destinations (when there are no charging lanes ahead). In this paper, we study this power distribution scheduling problem.We provide solutions to handle this challenge and also achieve each of the following goals as much as possible: i) balancing the state of charge (SOC) of the EVs, ii) balancing the amount of stored power of the EVs, and iii) minimizing the total power charged. This paper is the first work that handles such a power distribution scheduling problem in WPT systems. Our extensive experiments on MatLab and Simulation for Urban MObility (SUMO) show the effectiveness of our scheduling solutions in achieving the different goals compared with other scheduling methods including first-come- first-serve and equal share.