The prediction and control of solidification induced microstructure is an important issue during the product/process design stage in the selective laser melting additive manufacturing. It helps to avoid undesirable microstructures and possibly additional required post heat treatment, consequently improving the quality of manufactured parts. However, the direct numerical simulation of microstructure formation in this process is computationally very expensive, even by employing the state-of-the-art available computational resources. In the present study, an indirect approach based on empirical law is employed to predict the solidification microstructure. For this purpose, the macro-scale nonlinear heat equation include phase change effect is solved using the conventional finite element method and the local cooling rate and thermal gradient within the freezing interval is computed accordingly for Ti6-Al4-V alloy. Then, this information is projected on the empirical solidification microstructure map of this alloy to predict local microstructure, and the effects of process parameters like the laser power, laser effective radius (laser focus), scanning speed and scanning strategy on the solidification microstructure are investigated. According to the results, by decreasing the laser power, increasing the effective laser radius and laser scanning speed, the resulted grains morphologies can be varied gradually from the columnar to mixed columnar and equiaxed and completely equiaxed microstructures.