A modified fractal growth model based on the deposition, diffusion, and aggregation (DDA) with cluster rotation is presented to simulate two-dimensional fractal aggregation on liquid surfaces. The mobility (including diffusion and rotation) of clusters is related to its mass, which is given by Dm = D0s-γD and θm = θ0s-γθ, respectively. We concentrate on revealing the details of the influence of deposition flux F, cluster diffusion factor γD and cluster rotation factor γθ on the dynamics of fractal aggregation on liquid surfaces. It is shown that the morphologies of clusters and values of cluster density and fractal dimension depend dramatically on the deposition flux and migration factors of clusters.