Direct sampling is an efficient information theory-based multipoint simulation method. To reduce the computational cost, many approaches have been proposed to speed up this simulation method. In this paper, an edge-based two-stage strategy is proposed to achieve speed-up. The proposed method first performs a simulation on a coarse grid and then detects edge cells in the simulation grid. Next, only edge cells are simulated, and the remaining cells are assigned the average value of the neighbouring simulated and hard data cells. The proposed method needs only one easily-interpreted parameter and can be combined with other existing acceleration methods for direct sampling, such as parallelization. Comparison experiments are performed on categorical, continuous and multivariate variables, including two-dimensional and three dimensional examples. The experimental results show that the proposed method can reduce the simulation time by almost half with minimal loss in terms of pattern reproduction.