In this paper we construct topological sigma models which include a po
tential and are related to twisted massive supersymmetric sigma models
. Contrary to a previous construction these models have no central cha
rge and do not require the manifold to admit a Killing vector. We use
the topological massive sigma model constructed here to simplify the c
alculation of the observables. Lastly it is noted that this model can
be viewed as interpolating between topological massless sigma models a
nd topological Landau-Ginzburg models.