An understanding of genetic principles and environmental factors affecting the growth traits is essential to implement optimal breeding and selection programs. Early growth is an indicator of future success in production and reproduction status of dairy animals. In this study, a total of 18,989 records of body weight were used to estimate genetic parameters of body weight at birth (BW), 3 months (3BW), 6 months (6BW), 9 months (9BW),12 months (12BW), 18 months (18BW), 24 months (24 BW), 30 months (3BW), and 36 months (36BW) in Murrah buffalo at ICAR-NDRI Karnal, Haryana, for the period 1974-2019. The genetic parameters were estimated using the average information restricted maximum likelihood (AIREML) procedure by excluding or including maternal effects. Six analytical models were fitted in order to optimize the model for each trait. The most appropriate univariate model was selected based on the log likelihood ratio test (LRT). Influencing factors like calf sex, period of birth, season of birth, and dam's parity were investigated. The results showed that the maternal genetic effects, in addition to direct additive effects, were important for unbiased and accurate genetic parameter estimates of growth traits in Murrah buffaloes. Total heritability estimates h2T1 for BW, 3BW, 6BW, 9BW, 12BW, 18BW, 24BW, 30BW, and 36BW were 0.25, 0.04, 0.14, 0.16, 0.10, 0.15, 0.21, 0.24, and 0.23, respectively. Maternal effect was significant for birth weight and accounted for 13% variation through maternal genetic and 5% variability through maternal permanent environmental effect. Maternal genetic effect was also important for other traits. However, it interfered with the estimates of variance ratios in live weight traits owing to large and negative covariance between direct and maternal genetic effects. Direct genetic correlations between body weight traits were positive and high ranging from 0.10 to 0.94. Results revealed that the Murrah herd has a sizable genetic variability for growth traits and hence, there is sufficient scope for selection for achieving better growth rate if selection in this direction is applied. Owing to higher positive genetic correlation of 6BW with later ages, the scope of indirect selection for optimum growth in later ages can be aimed at by selecting animals for their higher 6-month live weight.