Internet of Things (IoT) have been widely used in many fields including smart city, industry Internet and automatic driving. Because IoT end devices usually have only limited capability in computation and power supply, they are not suitable to execute energy-consuming computational tasks. In many cases, we need to offload computational tasks from IoT end devices to edge servers in order to save energy consumption on the end devices. This process is usually termed as computing offloading. In this paper, we study computing offloading in radio frequency identification (RFID) systems built with mobile readers. We analyze the energy consumption characteristics of different components in mobile RFID systems, based on which we propose a framework to perform energy-aware offloading for such systems. By using tag searching as an example, we illustrate how our framework can help offload computational intensive tasks to edge servers to save energy consumption on mobile readers while satisfying the constraint on total execution time. Simulation results shown that the energy consumption of mobile readers can be greatly reduced by using our offloading framework.