Driven significantly by JP Morgan's RiskMetrics system with exponentially weighted moving average (EWMA) forecasting, value-at-risk (VaR) has become a popularly used measurement of the extent to which a financial asset is subject to the risks present in financial markets. In this paper we propose a new approach named skewed-EWMA to forecasting the changing volatility and formulating an adaptive and efficient estimation procedure to forecast VaR. Differently from the standard-EWMA in JP Morgan's RiskMetrics derived from a Gaussian distribution and the robust-EWMA proposed by Guermat and Harris (2001) from a Laplace distribution, we motivate our skewed-EWMA procedure derived from an asymmetric Laplace distribution, with both skewness and heavy tails of financial return distributions taken into account and in particular adapting to the changing nature of skewness and heavy tails in financial practice by an EWMA based adaptive adjustment of a shape parameter in the distribution. Backtesting results show that our skewed-EWMA forecasting of VaR offers a viable improvement over both the standard-EWMA and the robust-EWMA estimators.