We can see several characteristics of an epic hero in Odysseus.
Let's start with the fact that Odysseus belonged to royalty, since he was the king of Itaca. Generally, epic heroes have royal, noble blood, just like Odysseus. Furthermore, he is a warrior, strong and honorable. He faces his battles with dignity and with strong leadership, which causes the admiration of many men who follow him.
Other characteristics of an epic hero that we can find in Odysseus are his beauty, bravery, wisdom, honesty, strength and the ability to travel through exotic and different places, so that he can achieve his goals.