In wireless rechargeable sensor networks (WRSN), it is very challenging to schedule the mobile charger (MC) to replenish energy for sensor nodes timely to avoid node energy starvation in the charging process, and reduce the charging cost of MC and the average charging delay. However, most of existing WRSN mobile energy replenishment schemes either cannot adapt to the dynamic and diversity energy consumption of sensor nodes in actual environment or leave out of consideration of the timeliness and fairness of charging response, which may result in both sensor node failure due to energy starvation and low charging performance. The node energy starvation issue will be worse when there is a large number of request nodes in the networks. This paper explores the energy starvation issue in mobile charging for WRSN and proposes an energy starvation avoidance online charging scheme (ESAOC). To avoid node energy starvation, ESAOC first calculates the current energy consumption rate of each node based on both its history statistics and real time energy consumption. Then, to each request node, ESAOC calculates the maximum tolerable charging delay and its shortest waiting time for charging under the assumption that only one node would be selected as the next charging node. By comparing these two values, it always chooses the nodes which make the least number of other request nodes that could suffer from energy starvation as the charging candidates. Simulation results demonstrate ESAOC can effectively solve the energy starvation problem with lower charging latency and charging cost in comparison with other existing online charging schemes.