The aim of the present study was to estimate (co)variance components and genetic parameters for average daily gain from birth to weaning (ADGa), weaning to 6 months (ADGb), weaning to 9 months (ADGc), 6 months to 9 months (ADGd) and corresponding Kleiber ratios (KRa, KRb, KRc and KRd) in Mehraban sheep. A derivative-free algorithm combined with a series of six univariate linear animal models was used to estimate phenotypic variance and its direct, maternal and residual components. In addition, bivariate analyses were done to estimate (co)variance components between traits. Estimates of direct heritability (h2) were 0.10, 0.11, 0.16, 0.09, 0.13, 0.13, 0.15 and 0.08 for ADGa, ADGb, ADGc, ADGd, KRa, KRb, KRc and KRd, respectively and indicate that in Mehraban sheep genes contribute very little to the variance of the growth rate and Kleiber ratio. Estimates of maternal heritability (m2) were 0.10, 0.08 and 0.05 for ADGa, KRa and KRb, respectively. Direct additive genetic correlations ranged from −0.32 (KRa-KRd) to 0.99 (ADGb-KRb) and phenotypic correlations ranged from −0.53 (ADGa- ADGd) to 0.99 (ADGa-KRa). Estimates of direct heritability and genetic correlations show that genetic improvement in efficiency of feed utilization through selection programmes is possible, though it would generate a relatively slow genetic progress.