This paper proposes a parameterized integral data-driven anti-disturbance predictive control (PIDAPC) method to stabilize the attitude takeover system of a space combination under systematic disturbances after space non-cooperative target capture. The proposed method consists of a unified identification approach for the linearized system parameters and the truncated remainder (which includes both dynamics nonlinear residual and disturbance), along with a parameterized integral predictive control method. The unified identification approach ensures accurate state predictions through basic function assumption and provides preliminary for disturbance rejection. The PIDAPC scheme governs system stability and reduces control signal chattering through the disturbance identification and rejection, while the parameterized integral operation further refines the control action. Numerical analyses examine the fitting and predictive errors concerning some key parameters. Simulations validate the stability of the PIDAPC method and demonstrate its effectiveness in control signal chattering reduction.