A fixed-frequency beam-scanning leaky-wave antenna (LWA) array with three switchable dual-polarized beams is proposed and experimentally demonstrated. The proposed LWA array consists of three groups of spoof surface plasmon polaritons (SPPs) LWAs with different modulation period lengths and a control circuit. Each group of SPPs LWAs can independently control the beam steering at a fixed frequency by loading varactor diodes. The proposed antenna can be configured in both multi-beam mode and single-beam mode, where the multi-beam mode with optional two or three dual-polarized beams. The beam width can be flexibly adjusted from narrow to wide by switching between multi-beam and single-beam states. The prototype of the proposed LWA array is fabricated and measured, and both simulation and experimental results show that the antenna can accomplish a fixed frequency beam scanning at an operating frequency of 3.3 to 3.8 GHz with a maximum scanning range of about 35° in multi-beam mode and about 55° in single-beam mode. It could be a promising candidate for application in the space–air–ground integrated network scenario in satellite communication and future 6G communication systems.