According to the invention, there is provided seed and plants of the corn variety designated CV723321. The invention thus relates to the plants, seeds and tissue cultures of the variety CV723321, and to methods for producing a corn plant produced by crossing a corn plant of variety CV723321 with itself or with another corn plant, such as a plant of another variety. The invention further relates to corn seeds and plants produced by crossing plants of variety CV723321 with plants of another variety, such as another inbred line. The invention further relates to the inbred and hybrid genetic complements of plants of variety CV723321.