In this research, Data of milk yield, fat and protein percentage of Khuzestani buffalo were used. The daily records of milk yield were collected in the south-west of Iran where buffalo experienced a hot climate. The data set was constructed with 8,123 records of 1,430 first lactation buffalo. A univariate random regression model (RR/CF) was applied to data. Regression of additive genetic effect based on Legendre polynomials from the day of lactation was considered in the model. The results showed that maximum residual variance for the milk and fat production was estimated at the beginning of the lactation period. The minimum amount of additive genetic variation of milk and fat traits was seen in the early lactation period and the maximum amount of the component was estimated at the end of the lactation period. The lowest heritability of the mentioned traits was at the beginning of the lactation period. The level of this parameter increased to mid-lactation and was at its maximum during the late months of lactation, then decreased to the end of lactation. The estimated additive genetic correlations between close test-days were higher than faraway test-day records for each milk yield and milk fat content. Based on the results of this study, a random regression model with fitting orders 3 and 4, seems to be suitable for additive covariance functions in order to analyze the milk test-day records of buffaloes.