"Fushigi na Peach Pie" was written by Kazumi "Zuzu" Yasui （安井かずみ）and composed by Kazuhiko Kato（加藤和彦）to be Mariya Takeuchi's（竹内まりや）4th single, released in February 1980. Takeuchi relates in the liner notes for her 4-disc Best album, "Expressions" (2008) that Yasui came all the way to the studio where Takeuchi was working to tell her that the song would be perfect for her. Yasui's instincts were right on the money since the song was the first one to break the Oricon Top 10 for the pop singer...right up to No. 3. It was even used as the commercial campaign song for Shiseido Cosmetics (any woman who is referred to as having "momohada" or peach skin is a very lucky young lady....apparently, Japanese peaches may not have any fuzz). And considering that Takeuchi's works at that time often touched upon American pop melodies with strange titles in the 50s and 60s ("How Much is That Doggy in the Window?"), the song made for a good fit. The single also first made its appearance on an album through Takeuchi's "Love Songs" from 1980.
As I mentioned in the entry for EPO's "Downtown"(also released in 1980), The Three Daughters of RCA (Takeuchi, EPO and Taeko Ohnuki) often helped out in the backing vocals for each other. And so, EPO lends her voice here.