In the process of spacecraft optical autonomous relative navigation, the accuracy and completeness of target observation data are crucial to ensure high-precision relative navigation. However, due to the interference of the complex external environment, these observation data are often affected by incompleteness or loss, so they need to be modeled and predicted, and because the observation model of the spacecraft is a nonlinear system, the traditional method of local linear approximation to solve it is no longer sufficient to satisfy the accuracy requirements of the autonomous relative navigation, and The Koopman operator converts the finite-dimensional nonlinear system into an infinite-dimensional linear system, which describes the evolution law of the global linear system. Therefore, this paper proposes a prediction method of spacecraft autonomous relative navigation system observation data based on Koopman operator. Firstly, we derive the phase space topology of the nonlinear observation model by leveraging the primary mode of the Koopman operator. This approach unveils the long-term evolution pattern of the observation model, offering crucial insights for model prediction. Secondly, the nonlinear observation model is projected into the Hilbert space using the observability function. Subsequently, a linear combination of Koopman modes, eigenvalues, and eigenfunctions is employed to achieve global linearization of the nonlinear observation model, thereby mitigating the loss of nonlinear information. Finally, the results of simulation experiments show that the method proposed in this manuscript significantly improves the prediction accuracy relative to the existing methods.