  We first determine the automorphism group of the twisted Heisenberg-Virasoro
vertex operator algebra $V_{\mathcal{L}}(\ell_{123},0)$.Then, for any integer
$t>1$, we introduce a new Lie algebra $\mathcal{L}_{t}$, and show that
$\sigma_{t}$-twisted $V_{\mathcal{L}}(\ell_{123},0)$($\ell_{2}=0$)-modules are
in one-to-one correspondence with restricted $\mathcal{L}_{t}$-modules of level
$\ell_{13}$, where $\sigma_{t}$ is an order $t$ automorphism of
$V_{\mathcal{L}}(\ell_{123},0)$. At the end, we give a complete list of
irreducible $\sigma_{t}$-twisted
$V_{\mathcal{L}}(\ell_{123},0)$($\ell_{2}=0$)-modules.
