Genetic parameters for average daily gain from birth to weaning (ADGa), birth to 6 months (ADGb), weaning to 6 months (ADGc), weaning to yearling age (ADGd), and corresponding Kleiber ratios (KRa, KRb, KRc, and KRd) were estimated by using records of 3,533 Zandi lambs, descendent of 163 sires and 1265 dams, born between 1991 and 2005 at the Zandi Sheep Breeding Station at Khojir National Park, Tehran, Iran. A derivative-free algorithm combined with a series of six single-trait 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 (h(2)) were 0.11, 0.15, 0.09, 0.10, 0.10, 0.10, 0.06, and 0.07 for ADGa, ADGb, ADGc, ADGd, KRa, KRb, KRc, and KRd, respectively, thereby indicating the presence of low additive genetic variation for growth rate and Kleiber ratio in this population of Zandi sheep. Maternal genetic component was found to be significant on ADGa and KRa and contributed 3% and 5%, respectively, in total phenotypic variance of ADGa and KRa. A widespread range of genetic correlations among traits studied was observed. Except for negative genetic correlations between ADGa and KRc, ADGa and KRd, and between KRa and KRc, in other cases, genetic correlations were positive and moderate to very high. Phenotypic correlations ranged from -0.49 (ADGa/KRd) to 0.94 (ADGc/KRc). These results indicate that selecting for improved growth rate or Kleiber ratio in Zandi sheep would generate a relatively slow genetic progress.