A numerical investigation of the evaporation process of a water liquid droplet on the hot surface that has microstructure is presented. The microstructure is formed out of a uni-directionally solidified alloy, the composition of the alloy being exposed to the direction of heat flow by corrosion. The structure is considered as numerous micro-pin fins. The droplet instantly penetrated through the structure of which has a specific pin height after the placement of the drop. The kinetics of the penetration is described by R2 ∝tn. In the equation R is the radius of wet stain, and the power n is typically about 0.3. The evaporation process involved in the droplet penetration is classified into the four stages. The governing equations on each stage are solved numerically using the finite-difference procedure. The analysis is simplified by assuming the surface temperature to be constant during droplet evaporation. The simulated surface temperature is lower than 373 K. The results are compared with available experimental data indicating the outcome of the droplet lifetime and the droplet shape during evaporation. The computational model provides the additional information for the effects of the fin height and initial droplet diameter.