It's not a word on its own, but rather a part of a word that is attached to the beginning of another word to modify its meaning.
For example:
* Pseudo-science (fake science)
* Pseudo-intellectual (someone who pretends to be intellectual)
* Pseudo-history (false history)
Therefore, the part of speech of "pseudo" depends on the word it is attached to. For example, in "pseudo-science", "pseudo" is a prefix modifying the noun "science".