  Let $F$ be a non-archimedean local field of residue characteristic $p\neq 2$.
Let $G$ be a connected reductive group over $F$ that splits over a tamely
ramified extension of $F$. Yu constructed types which are called tame
supercuspidal types and conjectured that Hecke algebras associated with these
types are isomorphic to Hecke algebras associated with depth-zero types of some
twisted Levi subgroups of $G$. In this paper, we prove this conjecture. We also
prove that the Hecke algebra associated with a regular supercuspidal type is
isomorphic to the group algebra of a certain abelian group.
