The space-ground integrated network appears to be a promising solution for providing global coverage and broadband communications. Over the past several years, many pioneering research works toward space-ground integrated networks have emerged. However, it has been noticed that most existing research works have neglected the impact of satellite gateway placement on network reliability, in particular, not considering the practical capacity constraint on satellite links. In light of this, we study in this article the gateway placement problem with capacity constraint in the space-ground integrated network, and propose an enumeration scheme and a heuristic greedy scheme as our solutions. Extensive numerical results validate the efficacy of our proposed strategies.