There is the resonant propagation phenomenon of acoustic wave in bubbly liquid, i.e., the attenuation coefficient and the velocity of acoustic wave in range of resonant frequencies of bubbles can become very large. In previous papers, generally adopted was a simplified assumption that there is a single type of bubble in a liquid. It restricts our understanding of the resonant propagation phenomenon. In this paper the resonant propagation of acoustic wave in a liquid with mixed bubbles is studied. Here, static radii of bubbles are different from each other. Research results show that there is a restraining effect of the resonant propagation of acoustic wave in liquid with mixed bubbles. The attenuation coefficient and the velocity of acoustic wave in the liquid with mixed bubbles are obviously less than those in the liquid containing bubbles with the same static radius. The nature of the restraining effect is that the resonant vibration of bubbles is weakened due to the interaction between bubbles with different static radii. Some important properties of the restraining effect are investigated for all kinds of liquid systems with mixed bubbles. Moreover, the effect of the viscosity and the rate of cavitation on the restraining effect are also studied. Research results are shown as follows. 1) Comparing with bigger bubbles, resonant characteristic quantities (such as the attenuation coefficient and the velocity of acoustic wave) caused by smaller bubbles can be reduced more obviously; 2) the efficiency of the restraining effect increases with the number of types of bubbles increasing, however, it will gradually reach to a stable value when the number of types of bubbles is large; 3) the bandwidth of the resonant absorption of acoustic wave is dramatically affected by the distribution function of the percentage of the number of bubbles. The bandwidth of the resonant absorption will become large as the percentage of the number of smaller bubbles increases.