  We study the gauge-covariance of the massless fermion propagator in reduced
Quantum Electrodynamics (QED). Starting from its value in some gauge, we
evaluate an all order expression for it in another gauge by means of the
Landau-Khalatnikov-Fradkin transformation. We find that the weak coupling
expansions thus derived are in perfect agreement with the exact calculations.
We also prove that the fermion anomalous dimension of reduced QED is gauge
invariant to all orders of perturbation theory except for the first one.
