The vibration of bubbles in bubbly liquids has been studied when the driving sound field is fixed. The radius of the bubble will change when the bubble is driven by a driving acoustic field for a short time. This small change of radius is then fed back to the scattering process of the bubbles driven by the driving acoustic field. Thus the compound acoustic field including the scattered field of the bubble can be obtained. Then the bubble is again driven into vibration for a short time. By repeating the same procedure, the bubble vibration and its radius variation are simulated by a numerical method. It is shown that in the case of numerous bubbles in the liquid the vibration of a bubble is different from the case of only a single bubble in it. Because numerous bubbles will show interactions between one another, the radius of the bubble will change in different manner. For different size and content of bubbles, the radius of the bubble changes according to the following rules. The radius will oscillate in the vicinity of the equilibrium position; the radius oscillation shows a periodic cavitation process; the radius will vibrate during one cycle of cavitation; then, the radius will increase and oscillate in the vicinity of a certain value. Therefore, it is necessary that the bubble content should be considered in analyzing the vibration of the bubble in a bubbly liquid under a driving sound field.