The purpose of this study is evaluation and improvement of production functions to estimate Alfalfa yields under different deficit irrigations conditions and determination of “production of yield - water use” in Qazvin plain. This investigation was applied by Factorial experiment in a randomized complete block design with four water treatments including E4, E3, E2, and E1, respectively, equal to 60, 90,120 and 150 mm evaporation from class A evaporation pan as irrigation period, with three replications at the Agricultural Research Station Qazvin Esmaeelabad which run for three years. Since irrigation water applied in different years varied, treatments were separated from T1 to T12. So production functions based on evapotranspiration data for each treatment are reviewed. The result show that water requirement of Alfalfa in total of growth period is 1678 mm, T1 treatment had maximum yield with 16830 kg/ha and T12 treatment had minimum yield with 10020 kg/ha. And According to Statistical match, Tafteh et al. (2013) method that estimates amount of plant response factor based on defined power coefficient, which estimated at monthly intervals by rate response coefficients, had minimum of root mean square error (RMSE) and normal root mean square error (NRMSE). And it had maximum amount of agreement index and the correlation coefficient (r2).The amount of Plant yield response factors were determined in Ordibehesht, Khordad, Tir, Mordad, Shahrivar and Mehr respectively, equal to 0.85, 0.9, 0.99, 1.1, 1.1, 1 and for initial growth