In order to improve the spectrum efficiency of the integrated satellite-terrestrial relay network （ISTRN）， the performance of ISTRN based on NOMA in the presence of multiple primary users （PUs） is investigated under the spectrum sharing environment. Specifically， the closed-form expressions of outage probability （OP） and ergodic capacity （EC） of the system under the interference constraint imposed by multiple adjacent PUs are derived. For further study， the asymptotic expression of OP under high signal-to-noise ratios （SNRs） is obtained. Finally， the theoretical derivation is verified by numerical simulation， and the influence of key parameters on system performance is analyzed.