High throughput satellite (HTS) has been identified as a key technology for improving communication capacity of satellite system. Recently, low earth orbit high throughput satellite (LEO-HTS) has attracted much attention because of its low latency and construction cost. However, LEO-HTS is power-limited when it passes through the shadow of the earth, which will affect the lifetime and capabilities of the satellite. This paper focuses on the problem of energy saving for multiple LEO-HTSs in the LEO-HTS constellation. A method of adaptive power allocation with multi-beam directivity control according to the traffic demand of user equipments (UEs) is proposed to save energy. In this case, an optimization model is established to minimize the transmission power of multiple LEO-HTSs. Then, an alternating optimization framework is introduced to iteratively solve the transmission power and multi-beam directivity of multiple LEO-HTSs. Finally, numerical results demonstrate that the proposed method can save energy more effectively than the traditional method in the scenario with high traffic demand and concentrated UE distribution.