Dear Mohammad,

I suppose If grain boundaries contain impurities with a good electrical conductivity (e. g. different metals) they will have the smaller resistance than volume of the grain.

It is a well-known fact, that you can add certain non-conducting fillers (typical alumina or silica) to polymer hydrogen ion conductors, and obtain an increase in overall conductivity. The explanation is ,that you get a more efficient charge separation at the interfaces between the ion conductor and the filler material.

In this case the grain boundaries have the higher conductivity.

With inherently conducting solids, the situation is often the opposite: Here a certain ion has a high mobility in the crystalline solid, but these ions are less mobile in the disordered interphases (the grain boundaries). 

A common rule from Solid State Physics is that the grain boundary "resistivity" Zgb is, usually, higher than the bulk semiconductor's resistivity Zb; this rule might "brake" in insulators such as oxides, chlorites, fluorites etc.

Also, research on resistivity of polycrystalline silicon (wafers) p-Si is a good example for your inquire. Moreover, doping may offer a good playground for rule's crossover investigations, (not only) in basic research.

There could also be a thermal effect. For instance, speaking of mechanical resistance in steels, there is a transition temperature called "equicohesion temperature". Grain boundaries are more resistant under this temperature while grains are more resistant above.