Ultrasonic transducers with broad bandwidth are considered to have high axial resolution and good ultrasound scanning flexibility for the clinical applications. The limitations of spatial resolution due to bandwidth are of great concern in ultrasound medical imaging. The method of acoustic impedance matching between the piezoelectric element and medium is commonly used to obtain broad bandwidth and high resolution. In this study, an optimized backing layer design was proposed to broaden the bandwidth by adding a tunable acoustic impedance matching layer of backing (AIMLB) between the backing layer and the piezoelectric ceramic element. The Mason equivalent circuit method was used to analyze the effect of the backing material composition and its structure on the bandwidth of the transducer. The optimized transducer was simulated using the finite-element method with the PZFlex software. Based on the PZFlex simulations, a 20-MHz ultrasonic transducer using the AIMLB with a bandwidth of approximately 92.29% was fabricated. The experimental results were in good agreement with the simulations. The ultrasonic imaging indicated that the designed ultrasonic transducer with an additional AIMLB had high performance with good imaging capability.