In this paper we present a stochastic volatility (SV) model assuming that the return shock has a skew-Student-t distribution. This allows a parsimonious, flexible treatment of skewness and heavy tails in the conditional distribution of returns. An efficient Markov chain Monte Carlo (MCMC) algorithm is developed and used for parameter estimation and forecasting. The MCMC method exploits a skew-normal mixture representation of the error distribution with a gamma distribution as the mixing distribution. The developed methodology is applied to the NASDAQ daily index returns. Bayesian model selection criteria as well as out-of-sample forecasting in a value-at-risk (VaR) study reveal that the SV model based on skew-Student-t distribution provides significant improvement in model fit as well as prediction to the NASDAQ index data over the usual normal model.