  We construct a class of non-weight modules over the twisted $N=2$
superconformal algebra $\T$. Let $\mathfrak{h}=\C L_0\oplus\C G_0$ be the
Cartan subalgebra of $\T$, and let $\mathfrak{t}=\C L_0$ be the Cartan
subalgebra of even part $\T_{\bar 0}$. These modules over $\T$ when restricted
to the $\mathfrak{h}$ are free of rank $1$ or when restricted to the
$\mathfrak{t}$ are free of rank $2$. We provide the sufficient and necessary
conditions for those modules being simple, as well as giving the sufficient and
necessary conditions for two $\T$-modules being isomorphic. We also compute the
action of an automorphism on them. Moreover, based on the weighting functor
introduced in \cite{N2}, a class of intermediate series modules $A_\sigma$ are
obtained. As a byproduct, we give a sufficient condition for two $\T$-modules
are not isomorphic.
