He sent the letter to those incarcerated in Velletri, a city south east of Rome.
The pontiff was responding to a letter that the prisoners had written to him earlier in the year.
They gave their letter to Bishop of Albano, Marcello Semeraro, during a pastoral visit, for him to pass on to the pope.
Pope Francis thanked the prisoners for thinking of him and told them that they and other people in similar situations were in his thoughts, according to Vatican Radio.
He added that he often tries to make visits to local prisons during his travels.
The Holy Father also said that during the Holy Year of Mercy there would be a jubilee for prisoners, saying that prisoners often lead a life "in which time seems both to be stopped, and to never end."
He finished by saying: "The true measure of time is not that of the clock; rather, the true measure of time is called hope."
He told the prisoners to keep hopeful and "always be certain that God loves you personally."
