The invention relates to the wheat cultivar designated HV9W08-1836. Provided by the invention are the seeds, plants and derivatives of the wheat cultivar HV9W08-1836. Also provided by the invention are tissue cultures of the wheat cultivar HV9W08-1836 and the plants regenerated therefrom. Still further provided by the invention are methods for producing wheat plants by crossing the wheat cultivar HV9W08-1836 with itself or another wheat cultivar and plants produced by such methods.