Definitions of anti-hero vary slightly from source to source, but a good working definition is that an anti-hero is a story's protagonist that doesn't adhere to the traditional characteristics of a hero. The anti-hero is generally more flawed than most characters and disturbs readers with those weaknesses. This hero type is generally someone that doesn't fit the trustworthy, courageous, and honest characteristics of a normal hero, yet we can't help but sympathize and root for the character. A good modern film example would be Riddick from the movie Pitch Black and following sequels. To be clear, Grendel, as portrayed in the original poem, is not an anti-hero. He is pure evil. Gardner really throws readers a curve in his retelling of this epic by showing readers that Grendel is not pure evil. For sure, Grendel still murders a lot of people and still eats them, but Grendel is also portrayed as someone with a heart and sense of humor. We are even given gut-wrenching quotes that show Grendel is a character with huge inner turmoil.

Why can't I have someone to talk to?

Gardner even gives readers the idea that Grendel is in a position not by his own choosing. Grendel is the unfortunate side effect of some long lost descendant; therefore, Grendel is living a curse. That curse causes him pain, suffering, isolation, and loneliness.

He told of an ancient feud between two brothers which split all the world between darkness and light. And I, Grendel, was the dark side, he said in effect. The terrible race God cursed.

Deep down, we know that Grendel is doing bad things; however, we also know that he can't always help it. The actions he is taking are still brave. He's stepping into battle with the threat of death. That's a standard hero affair.

Grendel is portrayed in Gardner's novel as an outsider, equally fascinated and repulsed by the society he observes Hrothgar build. Treated as a monster by the humans, even when he comes to make peace with them, Grendel becomes determined to humiliate Hrothgar and his best warrior, Unferth. The novel becomes the story of his quest to get vengeance on the humans who have slighted him, so that he becomes a kind of dark counterpart to Beowulf in the original poem, who arrives to avenge Hrothgar and seek fame and glory through combat.

Another aspect of Grendel's oppositional relationship to the Beowulf story is his complex relationship with song and poetry. Grendel is attracted to the Shaper, a bard in Hrothgar's court who tells stories of human glory, but soon begins to question the truth of these stories (and, by extension, of art itself). As the author of his own story, Grendel usurps the means by which human history is recorded and makes it his own.

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.