Ice crystal growth by diffusion of water vapor from supercooled liquid water is simulated with equationswritten in a surface-following coordinate system. This two-dimensional system, similar to“terrain-following coordinate system” used in meteorology and oceanography, consists of the one axispointing vertical and the other following the crystal geometry. It facilitates the introduction of the boundarycondition on the surface of ice crystal so that simplifies the algorithm for computer programming. Byintroducing the system, the growth of one branch of snow crystal is simulated smoothly in contrast to theprevious simulations adopting the ordinary rectangular coordinate system where it becomes bumpy. Also,while the rectangular coordinate system shows different growth rate and shape of ice crystal with gridresolution, those obtained from the surface-following coordinate system depend little on grid resolution.