To address the issue of degraded angle measurement accuracy in missile-borne monopulse radar due to reduced signal-to-clutter ratio in the difference channel under cluttered environments, a convex optimization-based design method for low-sidelobe difference beam pattern synthesis was proposed. Simulation examples of optimized low-sidelobe and sidelobe nulling patterns validate the feasibility of the proposed method. This method is applicable to missile-borne monopulse radar systems to mitigate ground/sea clutter interference and enhance angle measurement performance.