In the present research, performance records of Fars native chicken from years 1988 to 2002 were used. Studied traits were body weight at 12 weeks (BW12), age at sexual maturity (ASM) egg weight (EW) and egg number (EN). Variance Components and genetic, phenotype and environmental correlations were estimated using restriction maximum likelihood (REML) and Bayesian analysis method based on Gibbs sampling technique under univariate and multivariate animal model. Univariate estimation of heritabilities with REML for ASM, EW, EN and BW12 were 0.53, 0.63, 0.33 and 0.53, while, with multivariate model these values were 0.51, 0.64, 0.33 and 0.53, respectively.Heritabilities estimates with Bayesian analysis in univariate model for ASM, EW, EN and BW12 were 0.53, 0.63, 0.34 and 0.55, respectively, while with multivariate model were these values 0.56, 0.58, 0.33 and 0.55, respectively. Genetic and environmental correlations between BW12 and ASM using both methods were negative but phenotypic correlation was positive. Genetic, environmental and phenotypic correlations between BW12 and EW and EN with both methods were positive. The estimates between W12 and EW with REML were 0.5, 0.15 and 0.36, whereas with Bayesian were 0.43, 0.26 and 0.28, respectively. Those estimates between BW12 and EN with REML were 0.03, 0.15 and 0.1, respectively, whereas with Bayesian were 0.19, 0.23 and 0.19, respectively. The above mentioned correlations between ASM and EN were high and negative using both methods. It can be concluded that the estimation of the parameters evalvated using with these two methods are close together.