Cairn, whose focus on Greenland has intensified since a deal to reduce its stake in its Indian unit, said on Tuesday that the Gamma-1 well in the Northern section of its acreage did not find any oil or gas.
Drilling continued at another well, the Delta-1 well, the company said, but so far that well showed only minor indications of hydrocarbons.
The company has already been frustrated in Greenland this year, when the first well of its 2011 exploration programme, LF7-1, came up dry, illustrating the difficulties of finding oil in the vast, little-explored Arctic territory where Cairn holds extensive acreage.
Cairn is leading a charge into offshore Greenland, which explorers believe could hold billions of barrels of oil. Exxon Mobil (XOM.N), Husky Energy and others also plan to drill there.
Shares in Cairn fell 8.3 per cent after the announcement and it was the biggest faller on the FTSE 100 in early trading.
"So far the drilling programme in Greenland has yielded little encouragement," Oriel Securities analyst Richard Rose said, calling the result disappointing.