This article investigates the identification of attitude system of spacecraft, with a particular focus on dealing with non-cooperative target spacecraft. During the interception of non-cooperative targets, their parameters may be unknown. Following the capture of a non-cooperative target by the service spacecraft, the primary objective is to maintain steadiness in the attitude control of the combined spacecraft. Establishing a state-space approach to model the system is essential for this purpose. Owing to the uncertainty in the parameters of the combined spacecraft's attitude control system, system identification methods are necessary to determine these parameters. Initially, this study develops a mathematical model of the spacecraft attitude control system. Subsequently, utilizing the subspace identification method based on the multivariable output-error state-space (MOESP) algorithm, a state-space model that accurately represents the original system is derived by comparing the system's input and output data. The model's validity is verified by comparing the output responses of the model and the actual system under different typical input signal excitations, demonstrating that the established model meets the identification criteria.