  The properties of the momentum space quark propagator in Landau gauge are
examined for the overlap quark action in quenched lattice QCD. Numerical
calculations were done on two lattices with different lattice spacing $a$ and
similar physical volumes to explore the quark propagator in the continuum
limit. We have calculated the nonperturbative wavefunction renormalization
function $Z(p)$ and the nonperturbative mass function $M(p)$ for a variety of
bare quark masses and perform a simple linear extrapolation to the chiral
limit. We find the behaviour of $Z(p)$ and $M(p)$ in the chiral limit are in
good agreement between the two lattices.
