A field pea cultivar designated CDC 0001 is disclosed. The invention relates to the seeds of field pea cultivar CDC 0001, to the plants of field pea cultivar CDC 0001, to plant parts of field pea cultivar CDC 0001 and to methods for producing a field pea plant produced by crossing field pea cultivar CDC 0001 with itself or with another field pea cultivar. The invention also relates to methods for producing a field pea plant containing in its genetic material one or more transgenes and to the transgenic field pea plants and plant parts produced by those methods. This invention also relates to field pea cultivars or breeding cultivars and plant parts derived from field pea cultivar CDC 0001, to methods for producing other field pea cultivars, lines or plant parts derived from field pea cultivar CDC 0001 and to the field pea plants, varieties, and their parts derived from use of those methods. The invention further relates to hybrid field pea seeds, plants and plant parts produced by crossing field pea cultivar CDC 0001 with another field pea cultivar.