Matthew Paul Hockely made sexual and suggestive comments to the girl after adding her on Snapchat days after interviewing her over photographs that had been circulated at school.

The pair exchanged more than 1000 chat messages and 30 images over three weeks from July 30, 2019.

In messages photographed by the girl, the father-of-two wrote, "heading home to get naked and relax" and "rather be chillin with you".

In another he said, "I was so cold last night. Needed you to warm me up".

The former officer also commented on sexual interactions between older men and girls, invited the teenager on holiday, told her he slept naked and called her "beautiful" in some messages to her.

In one message he offered to fetch her from the train station, saying it would be their first daddy-daughter experience.

Hockley admitted to adding the teenager on social media and sending her messages, saying he was interested in her mother.

Over the weeks he was chatting to the teenager, the officer had a consensual "sexual encounter" with her mother, telling the court his marriage was "broken almost beyond repair" at the time.

He also referred to the encounter in a message to the teenager.

A jury found him guilty of using the internet to procure a child and grooming a child with intent to procure a sexual act.

Hockley was a senior constable working at the Inala Child Protection and Investigation Unit in Brisbane at the time he committed the crimes, but was stood down after being charged, before resigning late last year.

"The mere fact that a person who is a sworn officer would engage in this conduct is abhorrent," Brisbane District Court Judge Bernard Porter said on Tuesday, while sentencing him to at least eight months in jail.

"The less serious nature of (Hockley's) conduct comprised in the offending is offset by the extremely serious misuse of his position as a police officer and his serious abuse of the trust and confidence placed in him by the complainant and her mother at a time when they were both vulnerable."

Hockley "betrayed his oath by grooming a young woman who he had come into contact with while investigating offending by and against her," Judge Porter said.

Outside court, the teenager's mother thanked the prosecutor "for her tireless efforts" and investigators for restoring her faith in the police service.

"Meeting these detectives has made me realise that there are people in the police service that are there for the right reasons," she told reporters.

"I'm just happy that this chapter has been closed and we look forward to putting this traumatic event behind us.

"I'm so grateful my daughter came forward when she did."

Judge Porter handed Hockley a head sentence of two years in jail, with a non-parole period of eight months.

Australian Associated Press