  We describe the center of the Hecke algebra of a type attached to a Bernstein
block under some hypothesis. When $\bf G$ is a connected reductive group over
non-archimedean local field $F$ that splits over a tamely ramified extension of
$F$ and the residue characteristic of $F$ does not divide the order of the
absolute Weyl group of $\bf G$, the works of Kim-Yu and Fintzen associate a
type to each Bernstein block and our hypothesis is satisfied for such types. We
use our results to give a description of the Bernstein center of the Hecke
algebra $\mathcal{H}({\bf G } (F),K)$ when $K$ belongs to a nice family of
compact open subgroups of ${\bf G}(F)$ (which includes all the Moy-Prasad
filtrations of an Iwahori subgroup) via the theory of types.
