Records for Afshari sheep were retrieved from data collected between 2000 and 2005 at the Zanjan University experimental flock, at Zanjan, Iran. (Co)variance components and corresponding genetic parameters for birth weight (BW), weaning weight (WW), 6-month weight (W6), average daily gain from birth to weaning (ADGa), from birth to 6 months (ADGb), from weaning to 6 months (ADGc), Kleiber ratio at weaning (WWKR) and Kleiber ratio at 6 months of age (W6KR) were estimated using univariate and bivariate analyses by the DFREML procedure. The Kleiber ratio, defined as growth rate/metabolic weight, has been suggested to be a useful indicator of growth efficiency and an indirect selection criterion for feed conversion. Estimates of direct heritability (h2) were 0.23, 0.27, 0.11, 0.22, 0.07, 0.01, 0.13 and 0.06 for BW, WW, W6, ADGa, ADGb, ADGc, WWKR and W6KR, respectively. Maternal genetic effects represented a relatively large proportion of the total phenotypic variance for BW (m2 = 0.22), whereas maternal permanent environmental effects were significant for W6 (c2 = 0.15), ADGb (c2 = 0.16), ADGc (c2 = 0.14) and W6KR (c2 = 0.16). Results of bivariate analyses indicated the variable genetic correlations between traits. The largest positive genetic relationships were between adjacent measurements. The moderate estimates of h2 for early growth traits indicate that in Afshari sheep faster genetic improvement through selection is possible for these traits. In order to increase the efficiency of feed conversion, use of Kleiber ratio in selection programmes was recommended.