The electric vehicle driveline generates less vibration and noise compared to a conventional internal combustion engine vehicle, making it harder for the driver to perceive the vehicle’s operating status through driveline sounds, thereby diminishing driving engagement and experience. To compensate for the absence of engine sound in EV drivelines, Active Sound Design (ASD) technology has become a crucial method for drivetrain sound enhancement, with sound synthesis algorithms playing a key role in this process. Although pitch-shifting algorithms based on frequency shift principles can synthesize engine sounds, they suffer from spectral leakage and stuttering caused by sound splicing. To address these issues, a pitch-shifting synthesis algorithm (QCPS, Quadratic interpolation-based Continuous audio sample indexing Pitch Shifting algorithm) is proposed in this paper, which combines a quadratic interpolation method with a continuous audio sample indexing strategy. First, the frequency shift coefficient of the sound is calculated. Based on this coefficient, corresponding sound fragments are extracted from the original audio and processed using a pitch-shifting interpolation method to generate the target sound. Then, different interpolation methods are compared for their impact on sound synthesis quality. Meanwhile, a continuous audio sample indexing strategy is developed to ensure seamless sound output. Finally, a simulation program for the QCPS algorithm is developed, and an ASD verification test bench is set up to validate the sound synthesis performance of the proposed QCPS algorithm. The results show that the proposed pitch-shifting synthesis algorithm exhibits minimal spectral leakage and ensures smooth sound splicing. This paper provides an effective solution for compensating EV powertrain sound and enhancing the driving experience.