Is there any myth similar to the story of Beowulf?
You could go with a number of epic poems that share similar motifs. Some of the motifs include characters that are heroic, journeymen/women, and of course monsters. There are quite a few epic poems that involve a journey: The Odyssey, The Divine Comedy, and The Aeneid. In The Divine Comedy, the hero/journeyman is the Pilgrim. At the beginning of the first section, Inferno, the Pilgrim is geographically (or spiritually) lost. Virgil, a Roman poet who wrote The Aeneid, serves as the Pilgrim's guide through hell. There are differences but also some similarities.
Whereas Beowulf was in search of adventure, and to some extent glory, the Pilgrim is seeking spiritual or moral knowledge. The Pilgrim has a guide (Virgil) and Beowulf has Hrothgar, more of a host than a guide, but Hrothgar is the one who presents the challenge to Beowulf. But both the Pilgrim and Beowulf have to make a journey; Beowulf to Grendel's mother's lair and the Pilgrim through the circles of hell. Both adventures require the hero to be courageous. In the third canto of Inferno, the Pilgrim reads these words inscribed above the gateway:
Before me nothing but eternal things
Were made, and I endure eternally.
Abandon every hope, who enter here.
There are more than just a few myths with similar content like a hero with supernatural ability who saves people by ridding them of a monster. For example, in Greek mythology, Theseus ventures into King Minos' elaborate labrynth in order to slay the horrible minotaur that the king had been regularly appeasing with young victims sent into the maze to become a meal for the monster. Like Beowulf, Theseus possesses bravery, strength, and cunning, and he acts on behalf of the common good, to prevent the monster from devouring any more of the young people of Athens. Another similar feature between the two myths is the idea of the hero descending deep into the monster's lair; both Theseus and Beowulf must enter the depths of their enemy's hideout in order to vanquish him.