The scheme, which started six years ago, involves taking kids out into the countryside and introducing them to the Swedish love of nature, the association says.
"These youngsters have no natural links to outdoor life in Sweden and how we look at the countryside, like the freedom to roam. Many of them come from countries where it can even be dangerous to be out in the countryside", spokesman Magnus Rydholm told TT.
The latest project this year took place in Borlänge in central Sweden during the ongoing elk-hunting season. Up to 300 youngsters took part this year alone.
But reaction to the scheme has not only been positive, with one previous officer at the association getting threats online.
"There are a few dark forces that don't think like us, unfortunately", Magnus Rydholm says, "but our values are: openness, respect and responsibility. We are open to all, no matter the background or religion. We are working with these issues and will not give way just because some people think differently."
And the sound of the hunt itself can cause problems for some. Swedish Radio in Dalarna reports that some refugees living in asylum centres in central Dalarna have been concerned by the sounds of the rifles used in the local elk hunt.
"the women and children that live here come from a war zone, so the firing in the early morning can being back horrible memories from the war zone they were living in, it can cause panic attacks especially for the children", said one resident.