The Australian share market has closed higher, with the troubled energy sector enjoying a surprise rebound in oil prices.

At the close on Wednesday, the benchmark S&P/ASX200 index was 9.6 points, or 0.19 per cent, higher at 5,161.9, while the broader All Ordinaries index was up 9.6 points, or 0.19 per cent, at 5,140.6, according to preliminary figures.

On the ASX 24, the December share price index futures contract was six points higher at 5,160, with 113,988 contracts traded.