With the continuously increasing demand for broadband applications and services, underlay cognitive satellite-terrestrial networks, enabling to accommodate better wireless services within the scarce spectrum, have attracted tremendous attentions recently. In this network, satellite communications are allowed to operate in the frequency bands allocated to terrestrial networks under the interference constraints imposed by terrestrial network, which may lead to a performance degradation of the satellite network. To guarantee the performance of the primary terrestrial network as well as the secondary satellite network, we introduce the cooperation into cognitive satellite-terrestrial networks and investigate the performance of the new framework, i.e., cognitive satellite-terrestrial cooperative network (CSTCN). Specifically, by restricting the transmit power of satellite communications with interference power constraints imposed by terrestrial communications, we firstly obtain the received signal-to-interference-plus-noise ratio (SINR) of the considered network. Moreover, by employing the moment generating function (MGF) approach, closed-form expressions for symbol error rate (SER) and outage probability (OP) of the considered cognitive network are derived. The analytical results obtained in this paper can provide theoretical support for optimizing the performance of satellite-terrestrial networks.