The 48-year-old actor, who features in the political drama as American senator Gary Hart, took to Twitter to share the picture.
"Day 1. Principal photography. The Front Runner. #thefrontrunner @JasonReitman @BronStudios," Jackman captioned the photo, which shows him giving a speech.
The "Logan" star portrays Hart, whose presidential campaign in the year 1988 goes off tracks when he is caught up in a scandalous love affair with Donna Rice (played by Sara Paxton).
The film is based on Matt Bai's book "All the Truth Is Out: The Week Politics Went Tabloid".
The movie also features Vera Farmiga, Kaitlyn Dever, Molly Ephraim and J K Simmons.
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