Acoustic black hole (ABH) structure has been extensively used in vibration mitigation, noise reduction, energy harvesting and so on, owing to its unique sound wave trapping and energy concentration effects. Besides, ABH structure holds emerging potential in improving the performance of ultrasonic device and constructing multifunctional acoustic field. Hence, an ultrasonic mode-conversion transducer consisting of a longitudinal sandwich transducer and an ABH wedge radiant plate is proposed in this work, in order to explore the potential applications of ABH in ultrasonic levitation and multifunctional particle manipulation. The theoretical model of flexural vibration of the radiant plate is established by utilizing Timoshenko beam theory and transfer matrix method, and the calculated vibration frequencies are in good agreement with those obtained by finite element method (FEM). The electrical impedance frequency response characteristics, vibration modes and the near-field sound pressure distribution of the transducer in air are also simulated. The results indicate that the amplitude of the ABH wedge radiant plate increases stepwise, and the sound pressure exhibits a gradient distribution. A prototype of the transducer is fabricated and experimentally tested, confirming the accuracy of FEM simulations and the feasibility of the design approach. Finally, the result of the ultrasonic levitation experiment indicates that the ABH design can give rise to gradient distribution of sound pressure in standing wave sound field for achieving precise particle sorting.