<p>This study presents an inverse design method for optimizing electrode patterns on a planar piezoelectric transducer to achieve ultrasound focusing. Traditional lens-based methods suffer from energy loss, impedance mismatch, and limited focal control. To address these issues, we develop a density-based topology optimization framework using a fully coupled piezoelectric-acoustic finite element model. A novel parameterization scheme for electric potential boundary conditions is introduced to represent the ground and electrode patterns. The proposed method is validated under various design conditions, including electrode design surfaces and focal lengths. Results indicate that larger design areas and shorter focal lengths improve focusing performance. Furthermore, post-processed electrode patterns, derived from the optimized distribution, achieve nearly identical focusing performance to the ideal case, demonstrating the effectiveness and practicality of the proposed approach.</p>