The magazine "St Peter's Square" is published by St Peter's Cathedral and will appear monthly.
The first issue was presented on Monday.
The magazine deals with topics from the Church and around the world - with a focus on social problems such as poverty, migration and violence.
It is available around St Peter's Basilica, but can also be obtained by post.
In the first issue, the Pope replies to a letter from a grandmother who is worried about her unbaptised five-year-old granddaughter.
Francis writes to her: " Baptism cannot be forced on parents who do not want it for their children."
He advises affected grandparents to engage in dialogue with sensitivity.
"Accompany your children, talk to them, but without insisting on the baptism proposal," said the Pope. "Prayer will certainly help you. You will see."