This paper presents a phase-offset adjustment method for sidelobe suppression in co-frequency multi-beam systems. The proposed method addresses the issue of minor lobe superposition, which arises when multiple co-frequency beams are radiated simultaneously, leading to increased sidelobe levels and degraded communication performance. By optimizing the phase offsets of each beam, the proposed technique effectively minimizes the vector sum of array factors in the sidelobe region without requiring additional hardware for amplitude control. Theoretical analysis explains the underlying principle and the algorithm used to adjust phase offsets, ensuring effective suppression of sidelobes. Experimental results obtained from an implemented S-band fully-connected multi-beam system validate the effectiveness of the proposed method, showing a significant reduction in sidelobe levels compared to conventional amplitude-only tapering techniques.