Chester Bennington bought his new family home about 2 months before he hanged himself there ... adding another layer of mystery to his death.

Axar.az reports citing on tmz.com that, the Linkin Park frontman bought the Palos Verdes Estates house for $2.5 million back in June. The 5 bedroom, 4 bathroom house is in an affluent part of L.A. County famous for pristine neighborhoods and excellent public school system.

Everything about the 3,956 square foot pad says family home -- special nook perfect for game night, 3 outdoor decks, an expansive backyard with a spa and swimming pool.

The purchase falls in line with what Chester's LP band mates said -- that he'd spoken excitedly about future plans. Buying the perfect place for his family, but then taking his life there a month later just doesn't add up.

The Benningtons closed on the house 8 days after Chris Cornell's suicide ... leading some close friends to believe Chester's suicide decision was sudden and fueled by his grief.