  In this paper we investigate Lie bialgebra structures on a twisted
Schr\"{o}dinger-Virasoro type algebra $\LL$. All Lie bialgebra structures on
$\LL$ are triangular coboundary, which is different from the relative result on
the original Schr\"{o}dinger-Virasoro type Lie algebra. In particular, we find
for this Lie algebra that there are more hidden inner derivations from itself
to $\LL\otimes\LL$ and we develop one method to search them.
