Test day records of Holstein cows from 1996 to 2011 was used in this study. Data consisted of 1114734 test-day records of 138407 cows in 42 herds of first lactation in Iran. Data was edited by Foxpro9.0 software and deleted records less than 6 kg and more than 51 kg.Variance components and breeding values and genetic trend were estimated using random regression model and DMU software. The heterogeneity of the residual variance in days 5 to 305 of lactation was modeled using 12 stage of 25 days interval. Additive genetic and permanent environmental random effects for the first lactation curve were taken in to account by applying orthogonal legendre polynomials of order four in the model. The results showed that the lowest and highest additive genetic variances were at the beginning (30-55) and end of the lactation period (280-305), respectively and generally were 4.59±0.16 and 10.56±0.30. Permanent environmental variance was high at the beginning (5-30) and end of lactation period (280-305) so was 19/81±0/21 and 18.29±0.24, respectively.Heritability of milk was between 0.17(±0.006) and 0.26(±0.007), protein was between 0.089(±0.006) and 0.23(±0.008) and fat was between 0.094(±0.005) and 0.134(±0.005), respectively. Genetic, permanent and phenotypic correlation among test days decreased as the interval between consecutive test-day increased. Genetic correlations were positive and higher than phenotypic correlations at all days in lactation. Genetic trend for all 3 traits milk yield, protein and fat were 28.67±1.51, 0.93±0.04 and 0.9±0.02 kg in year, respectively. The result of this research showed that the genetic trend for milk yield was satisfied. It be concluded that animal breeding programs were on milk yield trait in these years. Keywords : Holstein cow, milk yield traits, random regression model, test- day record
