The cognitive hybrid satellite terrestrial networks (CHSTN) is regarded as an effective way to enhance the spectrum efficiency as well as mitigate the spectrum scarcity problem. In this paper, we introduce a non-orthogonal multiple access (NOMA) scheme, which has the ability to simultaneously serve multiple users, in the cognitive network to further improve the utilization of radio spectrum. With the help of Meijer-G functions, the analytical expression for ergodic capacity of the considered system is derived. Simulations are provided to show the advantage of introducing the NOMA scheme in the cognitive system and the effects of some parameters on the performance of the considered network.