Particle collision growth is significantly promoted by flow turbulence. We proposed new collision kernel models which can describe the turbulence effect. By comparing the model predictions with the predictions by direct numerical simulations (DNS), we could confirm the reliability of our model. We also developed a large-eddy simulation (LES) method involving our new model. Then we performed the LES for the particle growth in a turbulent flow. Our LES prediction was compared to the DNS prediction. The comparison showed that our LES can well predict the particle growth in turbulence.