This study solves numerically the frost growth and densification on the surfaces of a fin-and-tube heat exchanger implemented in a biogas upgrading process. The upgrading process consists in removing undesirable components from the biogas such as water vapor, carbon dioxide, hydrogen sulfide and many others. Water could be removed by cryogenic condensation while frosting it at very low temperatures on the cold surfaces of a fin-and-tube heat exchanger. The thickness of the frost layer reduces the external flow passage surface and increases the biogas velocity, leading to higher pressure drop on the external side. The thermal resistance of the frost layer decreases the heat exchanger performance. The effect of the fin pitch is investigated in this study. About 70 % of the frost is captured from row 1 to 4 and the rest of the frost is captured between rows 5 to 18. Using a variable fin pitch delays as possible the frost formation on the fin surfaces. Thus, increasing the fin pitch tends to increase the frosting cycle duration and to decrease the external pressure drop. The numerical model developed for this study is valid for a low temperature range from 0 to -75 °C. This model has been validated by comparing numerical and experimental results.