Aviation has been one of the industries worst hit during the COVID-19 pandemic and airlines around the world expect it will take years before travel returns to pre-crisis levels.
The lessor did not say how many aircraft were affected by the agreement, although according to Airbus' website it currently has 43 A320neo and 10 A321neo jets on order to be delivered.
Under the agreement, advance payments to be made between now and three years' time will instead be due from 2024 onwards, Alafco said in a bourse filing.
An Airbus spokesman declined comment.
Earlier this month, Alafco said it had halved its order for 40 Boeing 737 jets after ending its legal claim over a cancelled order for the planes.
Alafco's owners include Kuwait Finance House, Gulf Investment Corporation and state airline Kuwait Airways, according to its website.
(Reporting by Alexander Cornwell; Editing by Amy Caren Daniel and Mark Potter)