The objective of the research is to estimate the function of Cotton production by using power function for one independent variable, choosing the double log model , then testing them by the first and the second statistical tests , They must be suitable of the agricultural production economic theory . The development of Cotton productivity for agricultural land in Iraq in the ( 2004– 2003 ) duration is 1679.84 kg/ha more than the productivity. of (1986-2003) duration, it is 1404.44 kg/ha , where as they are 2698.76 and 2698.76 kg/ha in ( 1968 – 1985 ) and (1950 – 1967 ) durations respectively . Thus, The Cotton productivity was incrased during the years . The economic derivatives of production function are estimated , they represent the marginal production and the average production functions , and production elasticities . The main result is the second stage of the law production of diminishing returns represented the Cotton production in Iraq . The productivity is low when it compared with the productivity of developed countries. Thus , the important suggestion is to do our best to reach higher production level.