  We microscopically examine the intergrain Josephson current in iron-pnictide
superconductors in order to solve the puzzle of why the intergrain current is
much lower than the intragrain one. The theory predicts that the intergrain
Josephson current is significantly reduced by the $\pm$s-wave symmetry when the
incoherent tunneling becomes predominant and the density of states and the gap
amplitude between two bands are identical. We find in such a situation that the
temperature dependence of the intergrain Josephson current shows an anomalously
flat curve over a wide temperature range. Finally, we suggest important points
for increasing the intergrain current.
