In this paper, we investigate the performance of a two-way hybrid satellite multi-terrestrial cooperative network with hardware impairments (HIs). Particularly, opportunistic relay selection scheme is employed in the considered network, which can substantially enhance the spectral efficiency and spatial diversity gain. By considering both the amplify-and-forward (AF) and decode-and-forward (DF) relay protocols, the closed-form expressions of the outage probability (OP) and throughput for the system are derived. Furthermore, in order to observe the effects of HIs level and the number of terrestrial relays on the system performance at high signal-to-noise ratios (SNRs), the asymptotic expressions of the system performance are also derived. Finally, computer results are presented to reveal the correctness of the analytical results.