This article designs a 20*20 beam-scanning leakage antenna square array operating at 32.1 GHz based on the amplitude weighting technique with the holographic antenna principle. We propose the microstrip line antenna cell with etched complementary split ring resonator (CSRR), use the liquid crystal(LC) material to realize the switching of the antenna cell state, and analyze the cell resonance characteristics. By arranging the units in a two-dimensional (2D) periodic manner and using amplitude weighting technology to control the state of each unit, beam scanning of the 2D antenna can be achieved. In the experimental process, we solve the problem of beam center depression due to the phase cancellation of front and back radiating waves, while a Python-HFSS (PH) control coding method is proposed to improve the coding efficiency during the design process. Simulation experiments show that the 2D antenna array can realize single-beam switching with its beam azimuth angle φ from − 36° to 40° and pitch angle θ from − 60° to 38°. After realizing the single-beam scanning, this paper establishes the theoretical system of multibeam scanning of 2D leakage antenna arrays based on amplitude weighting for the first time. After experimental verification, the antenna array can realize its dual/triple beam scanning with beam azimuth φ from − 30° to 30° and pitch angle θ from − 60° to 30°, which indicates that the theoretical system can be well applied to the design and application of 2D beam-scanning leakage antenna arrays.