Rumer Willis has lost her adorable little puppy -- and TMZ has learned, she's hitting the streets of L.A. desperately trying to find it.

Rumer adopted Indy Blue from a shelter a couple months ago -- a Terrier-Beagle mix -- but Indy recently took a wrong turn in the wilds of Hollywood, and now Rumer can't find him.

Rumer's been slamming up posters around her neighborhood hoping to track Indy down. So far, she's had no luck.

So if you live in the area -- keep an eye out.