High-intensity focused ultrasound (HIFU) treatment with cavitation bubbles has attracted much attention because they enhance the therapeutic efficacy of HIFU. Negative acoustic pressure is known toprimarily determine the cavitation threshold. However, it is hard to generate highly negative acoustic pressure over the cavitation threshold by ultrasonic focusing because of the nonlinear propagation. The sequence, starting with the second-harmonic superimposed pulse waves enhancing the peak negative pressure, and followed by those enhancing the peak positive pressure, demonstrated the highest efficiency in cavitation inception. A high speed camera showed that the negative-pressure enhanced pulse waves produced a small cloud of cavitated microbubbles at the first stage and that the positive-pressure enhanced pulse waves expanded the microbubble cloud at the second stage.