Rolling Stone magazine gave the album three out of five stars, calling it "proof that the Bieb is, verily, a musician, whose songs work even with the high-gloss production stripped away."
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Newspaper USA Today said Bieber was a "master at maximizing his material". But it added, "For people who've forgotten — or who never understood — the appeal of young performers like Bieber, 'Believe Acoustic' is a good place to hear it."
The other new songs are "I Would," a sweet love song, and "Yellow Raincoat," a mellow survival song with the singer crooning softly "cause the fame and the money and the girl will drive you crazy ... I'm thinking maybe just put on my raincoat."
If "Believe Acoustic" reaches No 1 in the Billboard 200 album chart next week, Bieber will become the youngest artist to have five No 1 albums under his belt. He would also be one of the few artists, including The Beatles and Jay-Z, to have a No 1 album each year for four consecutive years.
Bieber, who surpassed Lady Gaga earlier this month to become Twitter's most-followed person, will make his television hosting debut on "Saturday Night Live" on February 9, the night before the Grammy awards.
Bieber told Billboard he would not be attending the Grammy awards ceremony in Los Angeles.