"The 48-year-old Greek captain was just found dead," one coastguard official said.
The "Alpha 1" refuelling tanker, which sank off the Athens region's Elefsina refineries, was carrying 1,800 tonnes of crude oil and 235 tonnes of diesel when it foundered at around 10.30 a.m. (0830 GMT).
It may have sunk after hitting an old shipwreck, one official said, adding that there were no signs of any oil spill or pollution so far.