This paper focuses on the recursive identification of the time-varying state-space model of the on-orbit rigid-flexible coupling spacecraft caused by structural configuration change, and a recursive predictor-based subspace identification (RPBSID) method is applied to implement the online identification of the system model recursively. Comparing with the classical subspace algorithms such as the time-varying eigensystem realization algorithm (TV-ERA), the RPBSID method does not need to construct the corresponding Hankel matrix for each time instant when solving the state variables, and thereby reducing the amounts of data in the identification process. Furthermore, an adaptive filter is applied in this recursive algorithm and thus the ability of noise resistance is also increased. In numerical simulations, the time-varying state-space model of the spacecraft is estimated by using the RPBSID and TV-ERA approaches, and the system responses with respect to the test inputs for the two methods are also compared. The computed results of the test responses illustrate that the RPBSID algorithm can be used to effectively identify the time-varying state-space model parameters of the rigid-flexible coupling spacecraft, and the corresponding computational efficiency of the algorithm is also better than that of the classical identification method.