Eric Brevig directed the classic tale of adventure that stars Brendan Fraser, Josh Hutcherson, and Anita Briem.
The occasion marks the first release of a film authored in 3D. Previously, 3D releases have involved converting a conventionally shot film in post-production.
Family Day will also feature a screening of Walt Disney's Peter Pan in tribute to the late Disney animator Ollie Johnston who died in April.
Journey To The Centre Of The Earth 3D will open nationwide in 2D and 3D theatres on July 11.
The Los Angeles Film Festival is set to run from June 19-29.