With the rapid development of Integrated Satellite-Terrestrial Networks (ISTNs), large scale sensorsand wireless devices have the demand to access the wireless services, which is a new challenge to the spectrumefficiency and quality of service of ISTNs. Different from the conventional orthogonal multiple accesstechnology, Non-Orthogonal Multiple Access (NOMA) can provide communication guarantee for multiple usersin the same frequency. It is considered to be an effective technical path to improve the spectral efficiency ofISTNs, hence it has been widely studied. At present, most of the research on NOMA and ISTNs are investigatedunder perfect condition. Motivated by this condition, the performance of ISTNs with the more practicalsituation, i.e., imperfect Successive Interference Cancellation (SIC), channel estimation error and co-channelinterference, is studied in this paper. Considering that both satellite and terrestrial users use multiple antennas,the closed-form expression of ergodic capacity is derived, which verifies the impact of imperfect conditions onthe system performance. Meanwhile, Monte Carlo simulation is performed to verify the correctness of theoretical derivation results