This talk is concerned with a partially observed progressive optimal control problem of forward-backward stochastic differential equations (FBSDEs) with random jumps, where the control domain is not necessarily convex, and the control variable enters all the coefficients. In our model, the observation equation is not only driven by a Brownian motion but also a Poisson random measure, which also have correlated noises with the state equation. The partially observed global maximum principle is proved in another framework, which is different from but equivalent to the commonly used one. A partially observed linear-quadratic (LQ) progressive optimal control problem of FBSDEs with random jumps is investigated, by the maximum principle and stochastic filtering, as an example. Joint work with Dr. Yueyang Zheng.