The company said there were indications that the discovery, in a subsea prospect named Bagpuss, was "heavy oil".
Heavy oil is more viscous than other oil, and more difficult to extract from rock.
The well has been plugged and abandoned while further analysis is carried out.
Premier Oil's director of exploration and North Sea, Robin Allan, said: "The Bagpuss well has proven a significant volume of oil in place.
"We will now work with our partners to carry out a full analysis of the hydrocarbons and reservoir encountered to ascertain whether commerciality can be established."
The find comes a month after oil firm EnQuest reported a new discovery in the Central North Sea.
The company announced the "encouraging" find after completing drilling at an Eagle exploration well in the Greater Kittiwake Area (GKA).
Premier Oil has announced a "significant" oil find in the Outer Moray Firth, following a drilling operation.