An iterative learning adaptive sliding mode control algorithm with precise estimation of unknown parameters is proposed for a class of uncertain fully actuated systems with repetitive motions. By designing a desired trajectory of the tracking error, the strict requirement on the system initial condition is relaxed and the system is ensured to be on the sliding mode surface at the initial moment, which eliminates the reaching phase of the sliding mode and is beneficial for improving the robustness of the system. By constructing a set of low-pass filters and introducing forgetting factors and the normalization technique, the parameter estimation errors are reconstructed, and then the reconstruction results are utilized to design the differential-difference adaptive laws. Based on the Lyapunov theory, an iterative learning adaptive sliding mode control algorithm is designed, and it is proved that all signals of the closed-loop system are bounded, and the tracking errors and the parameter estimation errors asymptotically converge to zero. Finally, the proposed iterative learning adaptive sliding mode control algorithm is applied to the fly-around control of spacecraft, and the effectiveness of the obtained results is verified via numerical simulations.