This paper examines reliable and energy-efficient transmission in low earth orbit (LEO) satellite communication systems. In particular, we analyze the link transmission characteristics of the LEO satellite to the ground user and model the channel as a combination of large-scale fading and small-scale fading. Based on this, we consider an incremental redundancy hybrid automatic repeat request (IR-HARQ) technique with a variable-power allocation method, and we call it the IR-HARQ-VPA scheme. In this method, the outage probability after each IR-HARQ round can be obtained through numerical integration based on the fast Fourier transform (NI-FFT). This method is suitable for any number of HARQ transmission rounds and can improve the accuracy compared with previous approximation methods. In addition, variable-power allocation based on the genetic algorithm (VPA-GA) is introduced to reduce the energy consumption. The simulation results show that the proposed IR-HARQ-VPA scheme cannot only meet the requirements of transmission reliability but also achieves higher energy efficiency than IR-HARQ with equal power (IR-HARQ-EP) transmission and a previously proposed variable-power allocation method. Moreover, the simulation results in a LEO satellite communication window also confirm the effectiveness of the proposed IR-HARQ-VPA scheme.