For a class of spatially interconnected systems with multiple nodes, an iterative learning control algorithm in specified finite frequency range is proposed. Firstly, the repetitively running multi-dimensional spatially interconnected system is transformed into a class of two-dimensional equivalent system along the spatial node distribution direction based on lifting technique. Then the iterative learning control law is designed to transform the controlled system into a linear repetitive process, and according to the spectral range of the desired output trajectory, the Kalman–Yakubovich–Popov (KYP) lemma is used to transform the system's frequency domain stability analysis and control law design problems into corresponding linear matrix inequalities (LMI), while ensuring the monotonic convergence of the output tracking error in the time domain and frequency domain. Finally, the effectiveness of the proposed algorithm is verified by the control simulation of active ladder circuit.