The elliptic Hecke algebras associated to the 1-codimensional
elliptic root systems have been defined by H. Yamada [10],
which are subalgebras of Cherednik's double affine Hecke algebras
[2, 3]. The elliptic Hecke algebras associated to the elliptic
root systems of type $X^{(1,1)}$ have been defined similarly
by the author [11] in terms of generators and relations associated
to the completed elliptic diagram. On the other hand, M. Kapranov
[6] has defined modified Cherednik algebras associated to the
double coset decomposition of the group schemes over 2-dimensional
local field. In this paper, we see that modified Cherednik
algebras are isomorphic to elliptic Hecke algebras of type
$X^{(1,1)}$.