  The effect of non-magnetic Zn impurity on superconductivity in
LaFe$_{1-y}$Zn$_y$AsO$_{1-x}$F$_x$ system is studied systematically. In the
presence of Zn impurity, the superconducting transition temperature increases
in the under-doped regime, remains unchanged in the optimally doped regime, and
is severely suppressed in the over-doped regime. Our results suggest a switch
of the symmetry of the superconducting order parameters from a $s$-wave to
$s_{\pm}$ or $d$-wave states as the charge carrier doping increases in
FeAs-based superconductors.
