This is an intriguing question because, while Beowulf is certainly an exciting hero, there really isn't sufficient evidence to know him as a well-rounded character.

The first thing to do is define what makes a round versus a static character. A static (or flat) character remains essentially the same throughout the literary work, while a round character changes and grows. Therein lies the quandry.

Beowulf, as an epic hero, displays all the admirable qualities a protagonist of his stature should: bravery, loyalty, generosity, selflessness, strength, wisdom, and leadership. This makes him admirable, but really doesn't make him unique. He is the same character at the end of the poem as he is at the beginning (okay, he's significantly older, but essentially, he is still the same epic hero.)

So, by definition, as likeable and admirable as Beowulf is, he is more of a static literary type than an actual round character.