Facility contracts and services manager Peter Craik said about 20,000 children in New Zealand had at least one parent in prison.
The national Storybook Dads programme - delivered by the Dunedin Methodist Mission - was designed to build the relationship between father and child, and encourage literacy.
Fathers serving time could choose, or write, a story appropriate for the age, gender and interests of their children.
The father learnt to read the story in an engaging way before being filmed reading the book so a DVD could be sent to their children.
The programme began in OCF in 2007 and a new version of the programme began in February this year.
In this version, the fathers create a game relating to the book he read on the DVD to their child.
Last week, nine men in the Milton facility graduated from the programme by creating stories about Matariki for their children.
Each year, the prisoners created stories for Christmas, Easter and Matariki.
A recent graduate, a prisoner who could not be named, said he started the programme after being moved to the facility.
''I got transferred from Auckland and being away from my daughter is really hard for me. Being able to do this programme helps me interact with her by reading her stories and making things for her like puzzles and games.''
The programme gave prisoners a chance to show their children they still loved them, despite being away from them, the prisoner said.
''My daughter really loves being able to put on the DVD and read a story with her daddy whenever she likes.''
Mr Craik said prisoners often became upset when talking about being absent from their children's lives.
Another prisoner said the programme allowed him to show his children he was thinking about them.
''It is a really fun way to keep in contact with your children, especially if you are from out of town and don't get to see them. It is better than sitting in a cell just thinking about them. It is better to be doing something.''
Mr Craik said the programme ''brings out the father in the offender'' and helped them relate to their children.
About 70% of prisoners had low literacy levels and a large part of the programme was about embedding literacy skills.
''It also incorporates learning about relationships, parenting, children's behaviour and positive modelling.''
Children watching their father read impacted positively on their literacy development.
OCF manager Jack Harrison said the facility was one of the first prisons to offer the programme and it had been popular with prisoners.
''It changes relationships - it's really positive.''
