occur-check, does nominal unification has it? In unification, there is a "occur-check".  Such as $X = a \, X$ fails to find a substitution for $X$ since it appears on right hand side too.
The first-order unification, higher-order unification all have occur-check.

the paper nominal unification described a kind of unification based on nominal concepts. But I did not mention "occur-check" at all.

So, I am thinking why? does it has occur-check?
Yes, it has the occur check. The ~variable transformation rule of nominal unification has a condition which states 

   provided X does not occur in t


what it is saying is exactly occur check.