The invention relates to the wheat cultivar designated WB6121. Provided by the invention are the seeds, plants and derivatives of the wheat cultivar WB6121. Also provided by the invention are tissue cultures of the wheat cultivar WB6121 and the plants regenerated therefrom. Still further provided by the invention are methods for producing wheat plants by crossing the wheat cultivar WB6121 with itself or another wheat cultivar and plants produced by such methods.