This paper studies the secrecy performance of non-orthogonal multiple access （NOMA）-based integrated satellite-terrestrial relay networks （ISTRNs）. In this study， colluding eavesdropping case is considered， namely， the eavesdroppers cooperate with each other to overhear the legitimate information. Specially， we derive the closed-form expression for the secrecy outage probability （SOP） of the considered NOMA-based ISTRNs for the colluding eavesdropping case. In order to obtain further insights at high signal-to-noise ratios （SNRs）， the asymptotic expression for the SOP is also given to provide an efficient mean to evaluate the benefit of NOMA scheme and the impact of colluding eavesdropping on SOP. The number of the eavesdroppers and the channel fading have great impact on the secrecy performance. Finally， numerical Monte Carlo （MC） results are given to verify the correctness of the theoretical results. The results can provide the theoretical extremum for the practical works.