Summary: A lattice Boltzmann method for two-phase fluid flows with large density ratios is presented. The method is applied to the simulations of binary droplet collisions for various Weber numbers of 20<\(We\)<80 and for impact parameters of \(0\leqslant B< 0.82\) at the Reynolds number of \(Re\)=2000. Two droplets with the same diameter are considered. The density ratio of the liquid to the gas is fixed at 50. Coalescence collision and two different types of separating collisions, namely reflexive and stretching separations, are simulated. The boundaries between the coalescence collision and both of the separating collisions are found and compared with an available theoretical prediction in good agreement. The mixing processes during separating collisions are also simulated for various impact parameters at \(We\approx 80\), and the relation between the mixing rate and the impact parameter is obtained.