Hydrocarbon production rates and distributions on ruthenium promoted alumina supported cobalt Fischer-Tropsch synthesis (FTS) catalyst were studied by the concept of two superimposed Anderson-Schulz-Flory (ASF) distributions. The results indicated that the characterizing growth probabilities α1 and α2 were strongly dependent on reaction conditions. By increasing the H2/CO partial pressure ratios and reaction temperatures, deviation from normal ASF distribution decreases and the double-α-ASF distribution changes into a straight line. Based on the concept of double-α-ASF distribution, a useful rate equation for the production of hydrocarbons under industrial reaction conditions is obtained.