  This paper introduces the notion of Hom-Lie color algebra, which is a natural
general- ization of Hom-Lie (super)algebras. Hom-Lie color algebras include
also as special cases Lie (super) algebras and Lie color algebras. We study the
homomorphism relation of Hom-Lie color algebras, and construct new algebras of
such kind by a \sigma-twist. Hom-Lie color admissible algebras are also defined
and investigated. They are finally classified via G-Hom-associative color
algebras, where G is a subgroup of the symmetric group S_3.
