According to poets.org, an epic poem is:
a long, often book-length, narrative in verse form that retells the heroic journey of a single person or a group of persons. Elements that typically distinguish epics include superhuman deeds, fabulous adventures, highly stylized language, and a blending of lyrical and dramatic traditions.
Beowulf qualifies as an epic poem on several of these criteria. First, it is book-length, and it is a story that is written in the verse format. It tells the tale of the main character, Beowulf’s, heroic journey to slay the monster and then much later kill the dragon. During the poem, he has several adventures and accomplishes nearly superhuman deeds, as when he kills Grendel.
Grendel is a monster that lives at the bottom of the swamp. One night, Grendel kills some of King Hrothgar’s soldiers while they are asleep. This leads the King’s people to fear Grendel, as the monster terrorizes them over a period of more than a decade. Not surprisingly, King Hrothgar wants to find a way to rid himself and his kingdom of the monster forever to escape Grendel’s monstrous, violent fury.
Beowulf learns about Grendel and leaves his home in Sweden to help King Hrothgar protect his kingdom and get rid of the monster. Beowulf has had many prior victories that make him the ideal person to tackle Grendel. Ultimately, Beowulf is victorious and kills the monster, who returns to the swamp to die.
This is not the end of the story, however. Despairing over the death of her son, Grendel’s mother wants to avenge his death, and Beowulf must do battle once again. Although there is peace for a period—Beowulf even ascends to the throne upon the death of the king—it is short-lived. Ultimately, Beowulf must do battle again against the dragon.
In short, reflecting its epic journeys and epic battles, plus the heroic actions of the protagonist Beowulf, the poem qualifies as an epic one. Moreover, as Beowulf proves himself to be a hero who voyages over a long journey to kill Grendel against odds that he will succeed, it is a story about an epic journey and epic undertaking.