Abstract: Data of 507 Holstein dairy cows were used to estimate covariance functions by the random regression model for test-day records of the first lactation as function-valued traits. The model with Legendre polynomials of age as independent variances was used restricted maximum likelihood employing the average information algorithm (AIREML). After estimating the covariance functions of the meta-meter, the 3-D graphs were made by the Excel. The result showed that covariance functions could reflect the change of genetic and permanent variation for test day records in continuous scale of age. When the order of polynomial fit M6-5-10, the changes for yields were described adequately and the 3-D graphs were smooth. What was more, a reduced order fit involved less parameters and smoothed out differences in estimates of covariance.