The invention provides seed and plants of the pea line designated DLSC709-1058. The invention thus relates to the plants, seeds and tissue cultures of pea line DLSC709-1058, and to methods for producing a pea plant produced by crossing a plant of pea line DLSC709-1058 with itself or with another pea 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 pea line DLSC709-1058, including the seed, pod, and gametes of such plants.