It issued a yellow severe weather warning for most of the country apart from the extreme north from noon on Sunday to noon on Monday.
The latest alert follows an amber warning for Storm Dudley on Wednesday and a yellow warning for Storm Eunice on Friday in Scotland, and red and amber warnings for England.
The warning also covers parts of Northern Ireland, north west England and north Wales.
A Met Office spokesperson said: “Another spell of very strong winds is expected in parts of Northern Ireland, Scotland and also some Irish Sea coasts.
"Winds could gust to 50-60mph inland and between 70 and 80mph for a time on the mountains and exposed coasts, with large waves expected as well.
"The strong winds will be accompanied by heavy, frequent and increasingly wintry showers, with blizzard conditions expected in the mountains, before conditions ease later on Monday.”