A rice hybrid designated HR140004 is disclosed. Seeds of rice hybrid HR140004 were deposited under the Budapest Treaty (ATCC Accession PTA-121604), the plants of rice hybrid HR140004 and methods for producing a rice plant by crossing the hybrid HR140004 with a plant of the same genotype, or rice plant not of the same genotype, are also disclosed. Methods of growing and producing blends of rice seeds including seeds of rice hybrid HR140004 are disclosed.