A coriander variety, designated CN CORI 6003, is disclosed. The invention relates to the seeds of coriander variety CN CORI 6003, to the plants of coriander variety CN CORI 6003 and to methods for producing a coriander plant by crossing the cultivar CN CORI 6003 with itself or another coriander variety. The invention further relates to methods for producing a coriander plant containing in its genetic material one or more transgenes and to the transgenic coriander plants and plant parts produced by those methods. This invention also relates to coriander varieties or breeding cultivars and plant parts derived from coriander variety CN CORI 6003, to methods for producing other coriander varieties, lines or plant parts derived from coriander variety CN CORI 6003 and to the coriander plants, varieties, and their parts derived from the use of those methods. The invention further relates to hybrid coriander seeds, plants, and plant parts produced by crossing cultivar CN CORI 6003 with another coriander variety.