A novel sweet corn hybrid plant, designated HMX4372BS is disclosed. The invention relates to the seeds of sweet corn hybrid HMX4372BS, to the plants and plant parts of sweet corn hybrid HMX4372BS, and to methods for producing a sweet corn plant by crossing the sweet corn hybrid HMX4372BS with itself or another sweet corn plant. The invention further relates to methods for producing a sweet corn plant containing in its genetic material one or more transgenes and to the transgenic plants produced by that method and to methods for producing other sweet corn plants derived from the sweet corn hybrid plant HMX4372BS.