Pellet fuel is considered a sustainable energy source. But the way it's used now seems to produce air pollution which I think should not happen in case of sustainable energy source. So is pellet sustainable energy source in the way it's used now?
It is possible to farm wood sustainably, or unsustainably. Both ways happen now.
It is possible to use wood pellets for energy while trapping particulate matter and other non-GHG pollutants. This sometimes happens, and sometimes it doesn't.
It is possible to dispose of the resulting post-combustion products in a way that returns the nutrients to agricultural soil. This sometimes happens, and sometimes it doesn't.
So are wood pellets a sustainable source of energy? Well, it depends.
Generally, the situation is becoming less sustainable. The demand for large scale electricity production with wood pellets is rising faster than their production, and ('fresh') trees are being used in their entirety for the production of pellets. Calculate the energy required for that production + worldwide transport and any ecological advantage quickly dwindles.
You can pull this Belgian overview article describing the European situation through Google translate, or read the (mostly English) sources from 2009-2012 mentioned at the bottom.
Note that the article mainly focuses on energy production; burning pellets for heat is 'better': we need an estimated 38 versus 5 years before the CO2 balance is restored when using wood pellets.
I think biofuels are extremely destructive to the planet due the the vast amounts of land required to produce a small amount of energy.