This paper evaluates the predictability of WTI light sweet crude oil futures by using the variance risk premium, i.e. the difference between model-free measures of implied and realized volatilities. Additional regressors known for their ability to explain crude oil futures prices are also considered, capturing macroeconomic, financial and oil-specific influences. The results indicate that the explanatory power of the (negative) variance risk premium on oil excess returns is particularly strong (up to 25% for the adjusted Rsquared across our regressions). It complements other financial (e.g. default spread) and oil-specific (e.g. US oil stocks) factors highlighted in previous literature.