We proposes a new Bayesian MCMC algorithm for dynamic stochastic copula models with dependence parameters as unobserved state variables and presents the performance of the proposed MCMC algorithm through simulations. Our MCMC algorithm draws the state variables with an acceptancerejection Metropolis-Hastings algorithm using the candidate generating probability density function obtained by approximating the probability density function of the observed variables to the normal distribution of the dependence parameter.As an empirical example,weanalyzedthe stochasticcopulamodels for the KOSPI index and the HSCE index (Hang Seng China enterprise index) returnsfromJanuary3,2003toDecember30,2014usingtheproposedalgorithm. The Bayesian inference and model comparison results of the stochastic copula models of Gaussian copula, Student t-copula, Clayton copula, Frank copula, rotated Gumbel copula, and Plackett copula showed that Student t-copula model couldbeselectedasthebestmodel.Thesemodelcomparisonsresultsimplythat even though Gaussian stochastic copula model can capture ��near asymptotic dependence��, there may exist extreme tail dependence that can not be captured by the Gaussian stochastic copula model.