Finite W-algebras are certain associative algebras arising in Lie theory. Each W-algebra is constructed from a pair of a semisimple Lie algebra $g$ and a nilpotent orbit $O$ in $g$, which is actually a quantum deformation of the Slodowy slice of $O$. In this talk, we will determine the structure of the centers of finite W-algebras in prime characteristic.  Then we prove that the Azumaya loci coincide with the smooth loci in the maximal spectrum of the centers,  normal varieties, which means the irreducible modules of maximal dimensions for finite W-algebras are just parameterized by the smooth points in the spectrum. This is a joint work with Yang Zeng.