We have successfully demonstrated highly responsive, curved piezoelectric micromachined ultrasonic transducers (pMUTs) based on a CMOS-compatible fabrication process using AlN (aluminum nitride) as the transduction material. Micro fabrication techniques have been used to control the radius of curvature of working diaphragms from 400~2000 μm and theoretical analysis have been developed for the optimal dimensions of the transducers to boost the electromechanical coupling and acoustic pressure. A prototype device made of a 2µm-thick AlN on a curved diaphragm with a nominal size of 140µm in diameter and a radius of curvature of 1065µm has been fabricated. The measured resonant frequency is 2.19MHz and DC response is 1.1nm/V, which is 50X higher than that of a planar device with the same nominal diameter. As such, this new class of curved pMUTs could dramatically enhance the responses of the state-of-art, planar pMUTs with high electromechanical coupling for various ultrasonic transduction applications, such as gesture recognition and medical imaging.