During the battle with Grendel's mother, there are numerous comments made by the poet to the effect that Beowulf is "wigena strengest": the strongest man. He is also described as "trusting to strength," in the knowledge that he is not at the same disadvantage as another mortal man in his battle against this supernatural being, however fearsome Grendel's mother may be. So, we know that the poet does set considerable store by Beowulf's great strength. As indicated in the previous answers, we also see this strength at play in Beowulf's fight with Grendel and in his furious manhandling of Grendel's head.
However, there is also cause to question how far Beowulf's belief in his own strength may be overstated. The idea of "ofermod" (over-ambition) in Beowulf has been the subject of much scholarship. At the end of the poem, Beowulf takes on the dragon on his own, but ultimately his belief in his own strength is insufficient to save him. In part, we are led to believe that this is because of his great age, and not a reflection on his bravery, but others have pointed to some of Beowulf's earlier boasts and questioned the truthfulness of them. Beowulf is strong, but is he truly superhumanly so? Early in the poem, Beowulf describes to Unferth how he held his breath for the entire duration of a swim beneath the ocean and a battle against several fierce seamonsters—perhaps another example of superhuman strength, but equally perhaps an expression of ofermod, or a typical meadhall boast that stretches the truth.