This paper presents a mathematical model to predict the behavior of frost formed on an one-dimensional fin of heat exchanger, considering fin heat conduction under frosting conditions. The computational domain consists of air-side, the frost layer, and fin region, and they are coupled to the frost layer. The frost behavior is more accurately predicted with fin heat conduction considered (Case A) than with constant fin surface temperature assumed (Case B). The results indicate that for Case B, the frost thickness and heat transfer are overpredicted in most regions of the fin, as compared with those for Case A. In addition, for Case A, the maximum frost thickness varies little with the fin length variations, and the extension of the fin length after 30mm contributes insignificantly to heat transfer.