For the twisted Virasoro-current algebra $/mathfrak{g}$, which is the semidirect sum of the
Virasoro algebra and the twisted Heisenberg algebra, we give a complete classification of
the simple weight modules of $/mathfrak{g}$ with finite weight multiplicities. In particular,
any such module is either a highest or lowest weight module, or a module of the intermediate
series. We also obtain a classification of unitary simple highest weight modules of
$/mathfrak{g}$. This is a joint work with Dong Liu and Limeng Xia.
