The Pink Floyd guitarist's adopted son was handed the jail term on Friday for his part in the student fee protests in London last year.
The Gilmour family's lawyer told The Evening Standard that they are "actively considering grounds for appeal".
Charlie Gilmour was arrested soon after the December 9 clashes on suspicion of violent disorder and attempted criminal damage, before being released on bail.
He was photographed hanging from a Union Flag on the Cenotaph during the protests, and was later accused of throwing a bin at a convoy of cars containing Prince Charles and smashing a window.
At the end of the trial, Judge Nicholas Price QC said: "Such outrageous and deeply offensive behaviour gives a clear indication of how out of control you were that day."
David Gilmour's former Pink Floyd bandmate Nick Mason recently revealed that the band may consider a reunion in the future.