It was taken from a tank in a remote location off the A713 north of Carsphairn.
Police are investigating the 1500 litre theft, which took palce between December 23 and January 4.
Constable Hayley Elliot at Castle Douglas said: “This theft took place during the festive holidays from a site which is at the Dunhill sub-station, north of Carsphairn.
It has clearly been a planned theft as a suitable vehicle would have been required to remove the fuel.”
She added: “We are keen to hear from anyone who may have been on the A713 road in the Carsphairn area over the festive period and who may have seen anything suspicious.
“We also want to hear from anyone in the area who may have had any strange callers at their door over this period.”
Anyone with information should call officers on 101.