Beowulf is an unusual hero because he does not seek his own glory directly. While he is certainly famed for his exploits, and he does not have false humility (Beowulf rightfully boasts of his exploits because they are true), he is also concerned with the lives of his own people and those of others. He initially travels to Hrothgar's mead hall because he wishes to stop Grendel's reign of terror; while Beowulf will be commended and praised afterwards, he explicitly explains that he seeks to help, not to gain glory.
From feelings least selfish
I am able to render counsel to Hrothgar,
How he, wise and worthy, may worst the destroyer,
If the anguish of sorrow should ever be lessened,
Comfort come to him, and care-waves grow cooler,
Or ever hereafter he agony suffer...
(Hall, Beowulf, gutenberg.org)
This is Beowulf's mode of operation; he seeks to offer his guidence and his unique abilities in the service of others. In this manner, he is lauded as a hero for his physical exploits and abilities, but in his own mind, he is simply using his natural talents to help others. Were there a way for Beowulf to help Hrothgar without actually battling Grendel, he would have use it; even if the problem were solved without Beowulf being the hero of the day, he would offer his help and leave without any bitter feelings. In this manner, Beowulf is both a folk hero -- seen as heroic by others because of his deeds -- and a genuinely good person, seeking to help others for their sake, not for his own.