This paper will establish a closed-coupled oscillator model of the wide bandwidth ultrasonic transducer for ultrasound image application. Referring to the acoustical impedance matching theorem, the bandwidth depend on different matching impedance of the matching layers is investigated, and then the wide bandwidth ultrasonic transducer can be obtained. In order to shorten the pulse-echo duration time, the acoustical impedance of the backing layer is tuned to fit the resolution requirement. MATLAB is implemented to model and simulate of the equivalent lumped circuit of the designed transducer. The simulated results of transmitting transfer function and pulse-echo insertion loss can agree with the experimental results. Although the modeling accuracy is a bit less than that of propagation wave, this closed-coupled oscillator model seems relatively simple and easy to understand and closer to the original physical properties of elements of transducers. It also provides a complete one-dimensional model for the transducer and can well describe the electromechanical characteristics of the transducer.