Flapping-wing micro air vehicles (FWMAVs) have been widely developed to pursue the flight performance of insects. However, the FWMAVs usually have limited flight time. This study aims to increase the flight time by designing energy-efficient trajectory in climbing flight, which is one of the most energy consuming flight modes. The climbing trajectory is designed in 2-dimensional space. The cost function is defined as the energy consumption per unit altitude. Finally, the designed trajectory is converted to the spiral trajectory in 3-dimensional space for climbing flight in a limited flight space.