TwoSixty Inc, an online phone management service backed by Y Combinator, announced today that it has launched — a version of its virtual phone service specifically for Canada.

The phone service is a lot like Google Voice — it gives companies phone numbers that employees and customers can access and manage from anywhere. The company is focusing on keeping the quality of each phone call high in order to compete with voice-over-Internet programs like Skype and now Google’s internal calling service in Gmail — both of which are cheaper than TellFi on a per-call basis.

The service is geared toward companies rather than typical consumers, which Google has targeted with Google Voice. To that end, TellFi features conference call lines, extensions to other phone numbers and voicemail transcription. Companies can also forward their calls to other phones and schedule calls at a certain time.

“It’s a virtual phone system for someone who owns a cupcake store to someone who’s not very technical,” said co-founder Conor Lee. “Google Voice has a lot of great features, but it isn’t appropriate for businesses.”

Each company can get a phone number for free for a year as part of the promotion for the new Canadian push. That includes 100 free minutes per month, and it costs 6 cents per minute after that. There are two premium subscriptions, one for $24 a month and one for $70 a month. The better the subscription, the more minutes and phone numbers each company gets. The company has already picked up around 100 early subscribers in Canada.

TellFi decided to move into Canada after Grand Central, an early player in online phone management, dropped its numbers in Canada. That’s because Google bought Grand Central in 2007 and eventually remade the service into Google Voice.

The telephony company is also one of the first companies to be backed by angel investors Yuri Milner and Ron Conway’s new Start Fund. Each company in the winter 2011 Y Combinator class has the option to take a $150,000 investment from Milner and Conway, which caused a bit of a stink among angel investors who might lose the chance to invest in promising Y Combinator companies. Y Combinator typically invests between $15,000 and $20,000 in each company for the first several months. Garry Tan, founder of Posterous, is an adviser to TwoSixty.