Genetic parameters of milk, fat, and protein yields were estimated in the first lactation of Holstein dairy cattle. The records were collected during the period 2006 to 2011 and analyzed fitting the random regression model. The data included 41178, 25397 and 18716 test-day records of milk, fat and protein yields, respectively that produced by 4746, 3437 and 2525 cows respectively. Fixed effects in model included herd-year-month of test day and age-season of calving. The fixed and random regressions were modeled with normalized Legendre polynomials and (co)variance components were estimated by Bayesian method and Gibbs sampling was used to obtain posterior distributions. Estimates of heritability for milk, fat and protein yields ranged from 0.18 to 0.26; 0.06 to 0.11 and 0.09 to 0.22, respectively. Heritabilities for 305-d milk, fat and protein yields were 0.36, 0.23 and 0.29, respectively. For milk and protein yields, heritabilities were lower at the early of lactation due to the trends of lower additive genetic variance, higher permanent environmental variance. Genetic correlations for milk, fat and protein yields ranged from 0.14 to 1.00; 0.39 to 1.00 and 0.27 to 1.00, respectively. Ranges of estimated breeding values for 305-d yield of milk, fat and protein yields were from -1194.48 to 1412.44; -210.57 to 271.22 and -194.08 to 203.25, respectively. According to the results of this study, random regression model seems to be a flexible and reliable procedure for the genetic evaluation of milk production traits and it can be useful in the breeding programs for Iranian dairy cattle
