This paper proposes an advanced two-dimensional method to simulate the microstructure of metallic dual-phase polycrystalline materials to enable accurate micro-mechanics computation. This is done by combining geometric and metallurgical principles to simulate microstructures that are closer to experimental observations than currently used methods. The method accounts for difference in grain growth velocities in different phases during solidification. If the ratio of grain growth velocities equals 1, the proposed method reduces to the currently used Voronoi tessellation method. If the ratio of grain growth velocities tends to 1, the method matches the physical situation of one grain type becoming embedded in the other grain type. The simulation results show that although the original grain core points are the same, the microstructure of the material will change with the ratio of grain growth velocities, including the lengths of the grain boundaries, the radii of curvature of the grain boundaries, and the triple point locations. Statistical analyses are conducted on the number of grain edges, grain diameter, grain area, and proportion of two phases of grains. Statistical analysis shows that the simulation results of the proposed method agree well with the experimental observation.