The hardware impairments of transceiver nodes generate signal distortions and degrade the secrecy performance of wireless communications systems. In this paper, we investigate the effect of hardware impairments on the secrecy outage probability of hybrid satellite-terrestrial relay systems (HSTRS). The source satellite transmits its signal to the terrestrial destination with the help of decode-and-forward (DF) terrestrial relays, while the eavesdropper attempts to tap the transmission from the terrestrial relays to destination. An optimal relay selection (ORS) scheme is proposed for enhancing the physical-layer security of HSTRS against hardware impairments. The traditional round-robin scheduling (RRS) is also considered for comparison purposes. We derive closed-form expressions of the secrecy outage probability for both the RRS and ORS schemes. Numerical results show that given certain hardware impairments, the secrecy outage performance of ORS scheme is better than that of the RRS. Additionally, as the number of terrestrial relays increases, the secrecy outage probability of proposed ORS scheme decreases significantly, demonstrating the advantage of exploiting relay selection against hardware impairments for HSTRS.