Type IV flextensional transducers do not have broadband characteristics due to the deep valley between their first- and second-order response curves arising from the sound pressure cancellation produced by the vibration in different areas of the shell. In this paper, the cause of the deep valley is examined by analyzing the equivalent radiated sound field of the transducer. Simplifying the three-dimensional vibration equation to a two-dimensional equation shows that the vibration state of the shell is related to the positive and negative curvature. Therefore, a variable-shell flextensional transducer with a negative curvature is proposed, which changes the second-order vibration of the transducer by introducing a negative curvature structure. The transducer avoids acoustic pressure cancellation, achieves broadband characteristics, and has continuous high efficiency in the frequency band. After optimization, a prototype of the transducer is fabricated and a pool test is completed. The test results show that the transducer realizes the coupling of the first three vibration mode, forming a broad band with an in-band fluctuation of less than 8 dB at 1200-5600 Hz, and the efficiencies of the first to third resonance peaks are 30.2 %, 16.6 %, and 9.4 %, respectively.