A multivariate stochastic volatility model with dynamic correlation and leverage effect is described and estimated. The matrix exponential transformation is used to keep the time-varying covariance matrices positive definite. An efficient Bayesian estimation method using Markov chain Monte Carlo is proposed. Of particular interest is our approach for sampling the latent state variables from the conditional posterior distribution, using a blocked multi-move Metropolis-Hastings sampling, in which the proposal density is derived from an approximating linear Gaussian state space model. The proposed model is applied to the daily stock price index, the Japanese bond price index, and the Yen/USD exchange rate returns data.