Recording companies fed up with people illegally downloading music have a possible solution: Add the cost of music to monthly phone bills.

Mobile phone operator Cricket Communications Inc. will introduce a new unlimited plan entitling people to talk, surf the Web, send text messages, stream video — and download music — to their hearts’ content. The service, dubbed Muve Music, is the first of its kind in the U.S.

“Muve Music is designed exclusively for the mobile phone so no computer is needed,” Cricket says at its website. “With Cricket’s Muve Music rate plan, there are no download fees, no monthly music subscriptions, no streaming music to impact customers’ data plans and no credit cards or contracts are required.”

The service will cost $55 per month when it launches in January with a catalog of music from major recording labels such as Universal Music Group, Warner Music Group, Sony Music Entertainment and EMI Music. Muve even includes unlimited use of the popular app Shazam, which identifies the name of a song that is playing near the phone.

The service will be limited at least initially to the Samsung Suede phone, which utilizes Google’s Android operating system.

On its own, a comparable music subscription service, from the likes of MOG, Rhapsody, Thumbplay and Rdio, costs $10 a month.

Under the Muve plan, phone owners won’t technically own the music they download. The music cannot be removed from the phone, for instance, and transferred to a computer or a digital music player such as an iPod.

And music will vanish if a subscriber cancels service.

That model dissuades cell phone customers from canceling, while recording labels receive an unspecified percentage of those $55-per-month subscriber fees.

Cricket has more than 5 million subscribers, which it describes as predominantly low income. Only half of them, for instance, are estimated to have computers in their homes.

Their customers, it says, aren’t likely to purchase songs or albums digitally through Apple Inc. or Amazon.com Inc., nor are they likely to subscribe to digital music services such as Rhapsody. The alternative for many people would be to download music illegally.

Cricket and music labels are hoping that Muve will provide an easier way for people to download music and entice them to begin paying for it.

The Samsung Suede ($199) will initially be the only phone that works with Muve. The phone can’t download apps, but it has a 3-inch touchscreen, much like the iPhone, and can surf the Web and access e-mail.

Although Cricket’s Muve Music plan is the first of its kind in the U.S., other companies have introduced similar plans internationally. In 2007, for instance, phone maker Nokia unveiled its “Comes with Music” plan, whose costs were baked into the monthly data and voice plans that subscribers were already used to paying. Like Cricket, the service was designed so that music couldn’t be loaded onto digital music players. In April, Nokia lifted that restriction, but only for Chinese customers.

Get the latest news alerts: Follow LTW at Twitter.