Abstract: ‍ ‍Nowadays， the Internet of Things （IoT） has been applied in various fields of the economy and society. However， due to the limitations of space and environment， the terrestrial IoT has shown a serious shortage of service capabilities in some application scenarios. To solve this problem， the 6th generation （6G） mobile networks， proposes to integrate satellite communication and terrestrial communication to achieve seamless global coverage. For satellite communications， satellites are usually powered by solar energy， resulting in limited energy. Therefore， the energy-efficient design of satellites is necessary for achieving high-quality communications in large-scale devices. This paper provides an energy-efficient non-orthogonal multiple access （NOMA） framework for 6G low earth orbit （LEO） satellite IoT， so as to support massive machine-type communications （mMTC） of IoT devices distributed over a very large area. Considering limited energy supply and partial channel state information （CSI） at the LEO satellite， an energy efficiency maximization optimization problem is formulated subject to power and signal-to-interference-plus-noise ratio （SINR） constraints. Since the formulated problem is mathematically intractable， by transforming the fractional-form problem to an equivalent subtractive-form optimization problem， an iterative-based robust joint beam design and power allocation algorithm is proposed to maximize the energy efficiency in the presence of channel uncertainty. Both theoretical analysis and simulation results validate the effectiveness and robustness of the proposed algorithm.