We investigate how a dynamical mass of a fermion is affected by a topologic
al mass of a gauge field in a Maxwell-Chern-Simons QED(3) coupled with a tw
o-component fermion. The dynamical mass and also a parity condensate are es
timated by using a nonperturbative Schwinger-Dyson method. In particular, w
e study a limit of vanishing the topological mass in detail and clarify a l
ink between theories with and without a Chern-Simons term in a nonperturbat
ive level.