Piezoelectric micromachined ultrasonic transducers (PMUTs) have attracted widespread attention due to their high performance, miniaturization, and easy integration with semiconductor processes. In this paper, a PMUT device based on high-performance and lead-free Na0.5Bi0.5TiO3-BaTiO3 (NBBT) piezoelectric single-crystal thin films was designed for the application of medical high-frequency ultrasonics. Three-dimensional modeling and analysis of PMUT elements on the proposed structure were performed via the finite element method. The relationship between structure configuration in terms of the top electrode and the cavity shape of the bottom was studied. The PMUT properties and its device performance, including resonant frequency, effective electromechanical coupling factor (keff2), and the static sensitivity of different device structures, were analyzed. In addition, by rotating the Euler Angle γ of the NBBT piezoelectric single-crystal film, the static sensitivity and keff2 of the model are improved to 1.34 when γ is rotated to 45 ± 5°. It was shown that the PMUT using rotated NBBT demonstrated an enhanced relative pulse-echo sensitivity of −46 dB and a bandwidth of 35% when the reflective surface was 200 μm. We conclude that the PMUT in accordance with an NBBT piezoelectric single-crystal film designed by simulation offers a high frequency, larger keff2, and high sensitivity, which provides application prospects in high-resolution and high-frequency medical ultrasonic imaging.