A soybean cultivar, designed SN76208, is disclosed. The invention relates to the seeds of soybean cultivar SN76208, to the plants of soybean SN76208 and to methods for producing a soybean plant produced by crossing the cultivar SN76208 with itself or another soybean variety. The invention further relates to hybrid soybean seeds and plants produced by crossing the cultivar SN76208 with another soybean cultivar.