  Dynamical mass generation of a two-component fermion in $QED_3$ with a
Chern-Simons term is investigated by solving the Schwinger-Dyson equation
formulated in the lowest ladder approximation. Dependence of the dynamical
fermion mass on a gauge-fixing parameter, a gauge coupling constant, and a
topological mass is examined by approximated analytical and also numerical
methods. The inclusion of the Chern-Simons term makes impossible to choose a
peculiar gauge in which a wave function renormalization is absent. The
numerical evaluation shows that the wave function renormalization is fairly
close to 1 in the Landau gauge. It means that this gauge is still a specific
gauge where the Ward-Takahashi identity is satisfied approximately. We also
find that the dynamical mass is almost constant if the topological mass is
larger than the coupling constant, while it decreases when the topological mass
is comparable to or smaller than the coupling constant and tends to the value
in $QED_3$ without the Chern-Simons term.
