Spacecraft control problems frequently require the latest model parameters to provide timely updates to the controller parameters. This study investigates the recursive identification problem in a the time-varying state-space model of an on-orbit rigid-flexible coupling spacecraft. An improved recursive predictor-based subspace identification (RPBSID) method is presented to increase on-orbit identification efficiency. Compared with the classical RPBSID and other subspace methods, the improved RPBSID applies the affine projection sign algorithm. Accordingly, the system state variables can be determined directly via recursive computation. Thus, the proposed algorithm does not require constructing the corresponding Hankel matrix or implementing singular value decomposition (SVD) at each time instant. Consequently, the amount of data used in the identification process is reduced, and the computational complexity of the original method is decreased. The time-varying state-space model of the spacecraft is estimated through numerical simulations using the classical RPBSID, improved RPBSID, and SVD-based approaches. The computational efficiency and accuracy of the three methods are compared for different system orders. Computed results of the test response demonstrate that the improved RPBSID algorithm not only achieves sufficient identification accuracy but also exhibits better computational efficiency than the classical methods in identifying the parameters of the spacecraft time-varying state-space model.