Lance Corporal Monifa Sterling was convicted of disobeying an order to remove three print-outs of a verse from Isaiah from her desk last year.
She said that no one had complained and the problem was her supervisor did not like 'the tone of the verse'.
She had displayed Isaiah 54:17, "No weapon formed against me shall prosper", on her table.
After being convicted of disobeying the order to remove the verse she was given a reduction in rank and a bad conduct discharge.
The Navy-Marine Corps Court of Criminal Appeals has already rejected her appeal claiming that displaying a verse does not constitute religious exercise.
Ms Sterling is now asking the Court of Appeals for the Armed Forces to look at the case.
Senior Counsel Mike Berry said: "If a service member has a right to display a secular poster, put an atheist bumper sticker on their car, or get a Star of David tattoo, then Lance Corporal Sterling has the right to display a small Bible verse on her computer monitor."
He claimed that it was "blatantly unconstitutional" to tell the corporal to remove the verse.
A decision on whether the case will be reviewed is expected later this year.