The preview clip mixes interviews with the real-life Zampherini, now 96, with film footage starring Skins actor Jack O'Connell in the lead role.
Jolie appears too, in the director's chair, despite not acting in the movie herself.
"The will to push through any obstacle, the drive never to give into defeat," Tom Brokaw narrates over 1936 Olympics footage of the 5000 metres.
"These are the virtues that define the Olympic spirit, epitomised in the incredible story of former Olympian and American hero, Louis Zampherini."
With a screenplay co-written by the Coen brothers, shooting for Unbroken has just finished in Australia.
Other cast members include Garrett Hedlund, Alex Russell, John Magaro, Finn Wittrock, Domhnall Gleeson and Japanese actor Miyavi.
The trailer closes with a motto from Zampherini himself: "Don't give up, don't give in, there's always an answer to everything."
- Independent