Heritabilities and Genetic correlations among weaning weight and carcass traits in Korean cattle (Hanwoo) were estimated in multivariate animal model using threshold model with Bayesian inference via Gibbs sampling (TM-GIBBS) and using average information algorithm with restricted maximum likelihood (AI-REML). Those estimates were compared with each other to find out genetic property of each trait according to analytic methodologies. Multivariate animal models were set up with maternal effects for weaning weight and additive genetic effects for all traits in this study and considered age of weaning and age of slaughtering as covariates. Data were 1762 records with missing traits and 3762 animals with pedigree from progeny test program by Agricultural Co-operative Federation and the National Livestock Research Institute in Rural Development Administration in Korea. It was enable to converge to relevant criteria point when average information method for likelihood function of parameters by second derivative and Fisher scoring iteration method was used. Furthermore, all parameter estimates using multivariate threshold model and Gibbs sampling also showed to a consistent property even though estimates were different with each other. Heritability estimates for weaning weight and carcass traits by TM-GIBBS were higher than those by AI-REML in Henderson`s MME. In special, heritability estimates of MS were 0.43∼0.65 within 95 confidential interval by TM-GIBBS and 0.351 by AI-REML. Genetic correlations between maternal genetic effects of WWT and direct genetic effects of MS were negatively estimated as -0.33 by TM-GIBBS and AI-REML methods. The correlations of breeding values for marbling score between by TM-GIBBS and by AI-REML were slightly lower as 0.966 in Pearson`s correlation and 0.970 in Spearman`s rank correlation than those for other traits in this study. This study showed that threshold model of categorical trait and other linear type traits were valid and adaptable to genetic evaluation in Korean cattle.