A composite anti-disturbance predictive control approach utilizing multi-dimensional Taylor network (MTN) is presented for a rigid spacecraft, aiming to mitigate the effects of multi-source disturbances and time-delay. First, construct the model of the rigid spacecraft based on mechanism model. Second, MTN model is used as the disturbance observer to represent the influence of the external disturbance. Third, it is necessary to devise the MTN predictive control law and formulate a recursive \(\tau\) -step-ahead MTN predictive model. Furthermore, the backpropagation (BP) algorithm, incorporating a momentum factor, will be employed as the learning mechanism for the MTNs. Finally, within the framework of composite hierarchical anti-disturbance control, the attitude control is executed, grounded on the principles of “feedforward compensation” and “feedback suppression”. Simulation experiment of the rigid spacecraft is introduced.