  In this paper, we consider which kind of invariant measure on hereditary
subshifts is not Gibbs measure. For the hereditary closure of a subshift
$(X,S)$, we prove that in some situation, the invariant measure $\nu*B_{p,1-p}$
can not be a Gibbs measure where $\nu$ is an invariant measure on $(X,S)$. As
an application, we show that for some $\B$-free subshifts, the unique
equilibrium state $\nu_\eta*B_{p,1-p}$ is not Gibbs measure.
