Many financial researches have paid attention to capturing a comovement of financial time series in risk management subjects. In this article, we propose a multivariate GARCH model using a skewed t copula that is chosen as one of the most flexible copula specifications. We also employ an $S_U$-normal distribution as a marginal distribution in the GARCH modelling. In practice, we provide simulation comparisons and empirical analyses generated by this combination of copula and margin. For the empirical application, we select KOPSI, KOSDAQ for stock price and yen/dollar, dollar/euro for exchange rate. Our proposed copula specification is compared with multivariate normal distribution and multivariate $S_U$-normal distribution models.