Five different animal models, which differ in whether or not taking maternal genetic effect into account were used for estimating genetic parameters of growth traits in Iranian Adani goats and were compared via Akaike information Criterion (AIC) and Bayesian Information Criterion (BIC). Random effects in these models included direct and maternal additive genetic effects with direct-maternal genetic covariance, maternal permanent environmental and residual effects. Using five models, both genetic parameters and trends were analyzed with the WOMBAT program. Direct heritability estimates from different multiple traits models differ and ranged from 0.33 to 0.65, 020 to 0.63, 0.15 to 0.42, 0.16 to 0.43 and 0.15 to 0.45 for model 1 to 5 respectively. Maternal heritability ranged from 0.02 to 0.19, 0.12 to 0.33, 0.03 to 0.12 and 0.08 to 0.27 for model 2 to 5 respectively. Results indicated that maternal genetic effect has significant influence on growth traits but direct-maternal genetic covariance was not significant. Genetic correlation estimates using appropriate model varied from 0.18 to 0.98. Genetic correlations between adjacent traits were high and decreased as the distance between them increased but always were positive. Phenotypic correlations followed a similar pattern but were lower than the corresponding genetic.