Based on the theory of acoustic propagation, the mechanism of longitudinal-torsional vibration (LTV) by the vibration rod with multiple diagonal slits (MDS) under single excitation was explored. Using finite element analysis method, the influence rules of the composite stepped horn’s structural parameters on the natural frequency were studied. And the horn of longitudinal-torsional vibration (LTV) with 20 kHz resonant frequency was designed. The research results indicate that longitudinal-torsional vibration (LTV) can be realized under single excitation of longitudinal vibration when resonant frequency is 20 498 Hz,and the amplitude varies periodically.The results can be applied in the design of acoustic system of ultrasonic machining with longitudinal-torsional vibration (LTV).