The invention provides seed and plants of the bean line designated SV6139GR. The invention thus relates to the plants, seeds and tissue cultures of bean line SV6139GR, and to methods for producing a bean plant produced by crossing a plant of bean line SV6139GR with itself or with another bean plant, such as a plant of another line. The invention further relates to seeds and plants produced by such crossing. The invention further relates to parts of a plant of bean line SV6139GR, including the pods and gametes of such plants.