In this paper, the high speed photography and the pressure measurement are used to study the propagation and focusing process of the underwater intensive acoustic pulse which is reflected from an ellipsoidal reflector. The experimental results indicate that the reflector contribute to both the sound energy focusing and the generation of a negative pressure portion of the intensive acoustic pulse, and the cavitation bubble cluster will be induced to grow accordingly. Based on the experimental results, a sound propagation model derived from Kirchhoff diffraction integral and the equation of bubble dynamics proposed by Qian and Xiao [Qian Z W and Xiao L 2003 Chin. Phys. Lett. 20 80; Qian Z W and Xiao L 2008 Chinese Physics B 17 3785] are used to numerically study the propagation of the intensive acoustic pulse and the bubble motion. The numerical results indicate that the "wake wave" and "edge wave" will evolve into the negative pressure portion of the intensive acoustic pulse in front of the far focus of the reflector and the "center wave" will evolve into the negative pressure part beyond the far focus of the reflector. When the bubble is subjected to the reflected wave, it will be compressed and oscillate periodically during the positive pressure phase, and it will expand during the negative pressure phase of the incident pulse. And after the reflected wave passes, the typical processes of expanding, collapsing and rebounding can be seen clearly from the photographs. The research results have practical significance for understanding the propagation characteristic of the underwater intensive acoustic pulse with an ellipsoidal reflector.