  For any additive subgroup $G$ of an arbitrary field $F$ of characteristic
zero, there corresponds a generalized Heisenberg-Virasoro algebra $L[G]$. Given
a total order of $G$ compatible with its group structure, and any
$h,h_I,c,c_I,c_{LI}\in F$, a Verma module $M(h,h_I,c,c_I,c_{LI})$ over $L[G]$
is defined. In the this note, the irreducibility of Verma modules
$M(h,h_I,c,c_I,c_{LI})$ is completely determined.
