This study was carried out at the ruminant research station of the General Commission for Agricultural Research / Ministry of Agriculture (in Abu Ghraib 20km west of Baghdad) from December 2018 to December/2020. The research included 200 records belonging to the Turkish and local Awassi sheep herd to estimate some genetic parameters (heritability, genetic and phenotypic correlations, and evaluate the Best Linear Unbiased Prediction (BLUP) for some productive traits (total milk production, lactation period, birth weight Weaning weight, average weight gain). The estimate of heritability were for the productive traits 0.19, 0.12, 0.25, 0.29, 0.25, respectively. The genetic correlation for the effective traits ranged between positive and highly significant (P<0.01) and not significant, as its coefficient ranged between 0.81 and 0.15. The phenotypic correlation of the productive traits ranged between positive and highly effective (P<0.01) and was not significant, as the coefficient ranged between 0.87 and 0.12 for the above effective characteristics. The values of the Best Linear Prediction (BLUP) for traits ranged 12.376. The lowest of which is -0.641.