A large set of Baluchi sheep growth data collected at Abbasabad Sheep Breeding Station, Mashhad, Khorasan Razavi, Iran, was used to estimate phenotypic and genetic parameters for growth rate from birth to weaning (GRa), weaning to six months of age (GRb), and weaning to 12 months of age (GRc) and corresponding Kleiber ratios (KRa, KRb, KRc), efficiency of growth (EFa, EFb, EFc) and relative growth rate (RGRa, RGRb, RGRc). Genetic parameters were estimated by REML procedure fitting a series of six univariate animal models including various combinations of maternal effects. The most appropriate model for each trait was determined by the Akaike Information Criterion (AIC). In addition, a multi-variate analysis was done to estimate (co)variance components between traits. Estimates of direct heritabilities (h2) were, respectively, 0.06, 0.03 and 0.10 for GRa, GRb, and GRc; 0.06, 0.06, and 0.05 for EFa, EFb and EFc; 0.07, 0.04 and 0.06 for KRa, KRb and KRc; and 0.07, 0.05 and 0.05 for RGRa, RGRb and RGRc. For traits measured in the pre-weaning growth phase, maternal genetic effect was significant. The estimates of maternal heritability (m2) for GRa, KRa, EFa and RGRa were 0.11, 0.11, 0.04 and 0.04, respectively. Estimates of the additive genetic coefficients of variation (CVA) were used as a measure of genetic variability and ranged between 1.68% (RGRa) and 14.67% (EFb). Genetic correlations between traits ranged from −0.81 (EFa-KRc) to 0.94 (ADGa-KRa) and phenotypic correlations ranged from −0.72 (KRa-EFc) to 0.99 (GRb-RGRb). Overall, results showed little additive genetic variation in growth rate or efficiency-related traits of Baluchi sheep, indicating little opportunity for genetic improvement of these traits in this breed through selection. In addition, significant maternal effects on traits related to pre-weaning growth indicated the importance of including maternal effects in genetic evaluation of traits measured early in life.