  We construct a Lax operator for the $G_2$-Calogero-Moser model by means of a
double reduction procedure. In the first reduction step we reduce the
$A_6$-model to a $B_3$-model with the help of an embedding of the $B_3$-root
system into the $A_6$-root system together with the specification of certain
coupling constants. The $G_2$-Lax operator is obtained thereafter by means of
an additional reduction by exploiting the embedding of the $G_2$-system into
the $B_3$-system. The degree of algebraically independent and non-vanishing
charges is found to be equal to the degrees of the corresponding Lie algebra.
