Space information networks are proposed to broaden the observation area and realize continuous information acquisition using satellites and high-altitude platform stations. Space information networks are able to enhance detection and transmission capabilities compared to the current single Earth observation satellite. The satellite–terrestrial network is an important component of the space information networks. Hence, the major contribution of this article is to propose a new transmitted link selection scheme in a satellite–terrestrial network. Switch-and-stay combining scheme is used by destination to have a trade-off between the complexity and efficiency. The satellite, terrestrial relays, and destination user are influenced by hardware impairments, respectively. The closed-form expressions for the outage probability and throughput are derived. In order to analyze the system performance at high signal-to-noise rate, the asymptotic expressions for the system performance are also derived to give a special view on the impact of hardware impairments on the considered network. What is more, numerical results are derived to verify the correctness of our analytical results.