Background: Capacitive micromachined ultrasonic transducers (CMUTs) is a promising component of mechanical-electrical-acoustical conversion, which shows valuable applications in non-distructive testing and obstacle detection fields. In order to study the influence of dimension parameters on the directivity of CMUTs, the three-dimensional multi-physics coupling model is proposed for CMUTs in this paper. Methods: The model combines multiple physical fields through finite element method (FEM), which is more efficient and accurate. The influence of dimension parameters on the transducer is studied from two aspects: the pitch between adjacent cells and cell number, respectively. Results: When increasing the pitch, the directivity becomes better if the pitch is less than half of the wavelength, the grating lobe and side lobe are aroused. However, the bandwidth at-3dB is reduced by up to 71.1% at the same time. When increasing the cell number, the better the direcitvity, while the change of the cell number has little effect on the bandwidth of the array. However, 5.4% frequency shift was caused due to the effective mass change of the transducer. Conclusion: In this study, a 3D model based on FEM is proposed for the influence of dimension parameter on CMUTs. The simulation results indicate that the directivity can be enhanced by chang-ing the dimension. At the same time, it also introduces other performance issues, such as bandwidth decrease and frequency shift through this approach. Therefore, the simulation proposed the guidance of CMUTs performance optimization and patented technology application work in the future.