Princess Cruises is cutting prices by up to £100 to make week-long sailings available from less than £500.
The discounts apply to more than 800 departures between December this year and May 2022.
The sale rates are available to book between May 1 and June 30.
A £50 per person deposit offer is also being made available.
The deals are being offered as the company seeks to drive interest in cruise holidays.
The offers cover itineraries from the UK, Europe and other worldwide destinations including Asia, the Caribbean, Panama Canal and Alaska.
Those from the UK are during the spring, summer and autumn next year to destinations across northern Europe, southern Europe, the Mediterranean and British Isles.
The revised rates start at £499pp cruise-only for a seven-night Caribbean cruise from Fort Lauderdale on Caribbean Princess from February 7, 2021 against a previous rate of £599.
Other rates start at £679pp for a seven-night sailing from Southampton by Grand Princess on November 15 next year.
A 14-night Med cruise from Southampton on Grand Princess departing on July 24 2021 starts at £1,499pp.