How is Grendel an anti-hero?

In short, Grendel, as he is portrayed in John Gardner's
Grendel, is a point of view that subverts the status
quo. 

Grendel reveals that humans fool themselves by
rewriting history, by applying meaning where meaning doesn't exist (in the signs of
the zodiac, for instance), by creating gods where they don't exist.  Humans constantly
lie to themselves in order to emotionally and mentally survive and continue to
live.

Grendel is the teacher of reality in the novel.  He
is the bringer of truth.  He is the destroyer of illusion.  He thinks about killing the
queen in order to teach the humans reality.  He refuses to kill Unferth and instead
carries him back to the mead hall, in order to destroy the myth of the
great, superhero-like hero.   

Grendel points out the
foibles and shortcomings of human society.  He is a rebel and an
outsider. 

These make him an
anti-hero.

At the same time, you should remember, he is
also an unreliable narrator and he, himself, takes on the role of his nemesis, the
Shaper.  Grendel becomes an artist, a rewriter, if you will.  He writes the novel.  He
tries his hand at poetry.  He embraces art, even though he despises it.  He both loves
and hates art.  And though Unferth is his goat, so to speak, he also reveals a kind of
nobility--a kind of heroism--in Unferth.  Humiliated, embarrassed, sinful (killed his
brother), Unferth is still the warrior who sleeps in front of the queen's door to
protect her. 

Maybe humans do lie to themselves in order to
survive.  But they do survive and endure.  The novel is about reality vs. art.  And art
wins.