  Leading electroweak corrections play an important role in precision
measurements of the strange form factors. We calculate the two-photon-exchange
(TPE) and $\gamma Z$-exchange corrections to the parity-violating asymmetry of
the elastic electron-proton scattering in a simple hadronic model including the
finite size of the proton. We find both can reach a few percent and are
comparable in size with the current experimental measurements of strange-quark
effects in the proton neutral weak current. The effect of $\gamma Z$-exchange
is in general larger than that of TPE, especially at low momentum transfer
$Q^2\le 1 GeV^2$. Their combined effects on the values of $G^s_E+\beta G^s_M$
extracted in recent experiments can be as large as -40% in certain kinematics.
