A Hobart man who sent sexually suggestive Facebook messages to a 13-year-old girl he befriended online has avoided jail.

The Supreme Court in Hobart heard Christopher Craig Banks befriended the girl on Facebook last September.

The pair exchanged more than 1,500 messages mainly through Facebook over the next two months.

The prosecution told the court Banks, 30, asked the girl for sex and "hot" photos and also offered to find her a younger boyfriend.

Banks pleaded guilty to communicating with intent to procure a person under 17 to engage in an unlawful sex act.

The court heard Banks has a psychotic illness and was charged after telling medical staff he had a teenage girlfriend.

Justice Peter Evans imposed a three month prison term, but suspended all of it.

Tasmania's Sexual Assault Support Service says such cases are not uncommon.

Spokeswoman Liz Little says the case should serve as a warning of the dangers of social media.

She says while it is increasingly common, awareness is increasing and more offenders are being caught.

"All parents and all young people should be aware that these types of sexual predators are out there places in terms of places like Facebook," she said.