Genetic improvement program will only be successful when accompanied by a good understanding of the influence of environmental factors, knowledge of the genetic parameters, and the genetic relationships between the traits of interest. Thus, this study aimed to evaluate the influence of non-genetic factors on growth traits and Kleiber ratios and to estimate genetic parameters for early growth traits in Dorper x indigenous sheep. The effects of fixed factors were analyzed by the general linear model procedure of SAS and the genetic parameters were estimated by AI-REML algorithm using a WOMBAT computer program fitted animal model. The log-likelihood ratio test was used for selecting the best-fitted model from four models. The overall least-squares means for birth weight (BW), weaning weight (3MW), six-months (6MW), nine-month (9MW), and yearling (12WT) were 3.03 ± 0.02, 14.5 ± 0.18, 20.4 ± 0.26, 24.8 ± 0.31, and 28.3 ± 0.40 kg, respectively. The overall least-square means for Kleiber ratio from birth to weaning (KR1), weaning to six-month (KR2), six to nine-month (KR3) and nine-month to yearling age (KR4) were 16.8 ± 0.10, 6.41 ± 0.17, 4.55 ± 0.21 and 3.38 ± 0.20 g/kg of metabolic weight, respectively. The inclusion of maternal genetic effect exerted a significant influence on BW and it explains 20% of the phenotypic variation. The total heritability (h2t) estimates for BW, 3MW, ADG1 and KR1 were 0.10, 0.14, 0.16 and 0.12, respectively. The phenotypic correlation varied from − 0.11 to 0.98 whereas the direct genetic correlation ranged from − 0.32 to 0.98. The mean inbreeding coefficient was 0.105% with annual rate of 0.02%. The heritability estimates for growth traits and Kleiber ratio suggests that slow genetic progress would be expected from the selection. However it is, integration of selection with crossbreeding program with this level of variation would enhance the genetic gain. Therefore, selection should be conducted based on breeding values estimated from multiple information sources to increases the selection response.