  A phenomenological theory of tunneling spectroscopy for Fe-pnictide
superconductors is developed by taking into consideration of asymmetric
interface scattering between particle and holes. It is shown that in consistent
with anti-phase $s^{\pm}$-wave pairing, appreciable zero-energy surface bound
states exist on the [100] surface of Fe-pnictide superconductors. However, in
contrast to the [110] bound states in $d$-wave cuprate superconductors, these
bound states arise as a result of non-conservation of momentum perpendicular to
the interface for tunneling electrons and the $s^{\pm}$ pairing, and hence they
can only exist in a small window ($\sim \pm 6^{\circ}$) in the orientation of
edges near [100] direction. Our results explain why zero-bias conductance peak
is often observed in tunneling spectroscopy and when it disappears, two
coherent peaks show up. These results provide unambiguous signals to test the
possible $s^{\pm}$-wave pairing in Fe-pnictide superconductors.
