  In this paper, the definition of Hom-Lie groups is given and one conntected
component of Lie group $GL(V)$, which is not a subgroup of $GL(V)$, is a
Hom-Lie group. More, we proved that there is a one-to-one relationship between
Hom-Lie groups and Hom-Lie algebras
$(\gl(V),[\cdot,\cdot]_\beta,\rm{Ad}_\beta)$. Next, we also proved that if
there is a Hom-Lie group homomorphism, then, there is a morphism between their
Hom-Lie algebras. Last, as an application, we use these results on Toda lattice
equation.
