  We compute the two-loop effective K\"ahler potential in three-dimensional N=2
supersymmetric electrodynamics with Chern-Simons kinetic term for the gauge
superfield. The effective action is constructed on the base of background field
method with one parametric family of gauges. In such an approach, the quadratic
part of quantum action mixes the gauge and matter quantum superfields yielding
the complications in the computations of the loop supergraphs. To avoid this
obstacle and preserve dependence on the gauge parameter we make a nonlocal
change of quantum matter superfields after which the propagator is
diagonalized, however the new vertices have appeared. We fix the suitable
background and develop the efficient procedure of calculating the two-loop
supergraphs with the new vertices. We compute the divergent and finite parts of
the superfield effective action, find the two-loop effective K\"ahler potential
and show that it does not depend on the gauge parameter.
