The actor says the script contains "many weeks worth of notes and ideas" as he makes an appeal for help to get it back.
The actor said a bag taken in the theft, which happened on Sunday evening, also contained his children's medical cards.
In an appeal for help on Twitter, he said: "In the unlikely chance that anyone knows who broke into my car tonight and stole my bag, please try and persuade them to at least return my script.
"Many weeks worth of notes and ideas. And perhaps my children's medical cards. Coach Films, Ealing St Mary's Ealing Green W5 5EN*"
Grant did not say what the script was for or where he had left his car when the break-in took place.
The star, most famous for his roles in Richard Curtis romantic comedies Love Actually, Four Weddings And A Funeral and Notting Hill, recently starred in A Very English Scandal.
He played former Liberal Party leader Jeremy Thorpe, who was accused of conspiring to murder his alleged former lover Norman Scott, in the series, and was nominated for a Golden Globe award.
He is currently working on Toff Guys, a Guy Ritchie film about a British drug lord, as well as HBO series The Undoing, also starring Nicole Kidman, according to movie and TV database IMDB.