This question comes up fairly often, and it never ceases to amaze me...
All human beings, regardless of diet, have the same nutritional needs, for all intents and purposes.
Vegetarians/vegans have the same nutritional needs as those who eat an omnivorous diet.
Maybe it should be pointed out that hominids evolved eating a mostly vegan diet, with only a few insects, small reptiles or amphibians, here and there. ...Whatever we could grab with our hands. Human beings did not arrive on earth magically knowing how to make and use tools, or with knowledge of agriculture or animal husbandry.
So, think about what you could grab with your hands, and that's what your ancestors ate. That would be things like fruit, nuts, berries, roots, insects, small & slow animals. Paleontologists also believe humans scavenged a bit, as well. (I.E. coming across a leopard's kill hidden in a tree) As an early hominid, if you did come across a predator's larger kill, you'd have to chew the flesh right off the carcass. (remember, no tools)
Tool use, agriculture and animal domestication are relatively recent, in evolutionary terms. For the tens of thousands of years of hominid evolution prior to tool use, we ate what we could grab with our hands. We certainly weren't bringing down antelope or buffalo with our bare hands.
I have been vegan for over a decade, and was a vegetarian for about a decade before that. I am supremely healthy and get everything my body needs, from my vegan diet. Humans simply don't "need" animal products to not only survive, but to thrive. That said, I'm not against eating meat, per se. I am vegan because I oppose domestication, captivity, cruelty, and factory farming. I wish all living beings were free to live the autonomous lives nature and evolution intended.