A novel maize variety designated X13C704HR and seed, plants and plant parts thereof, produced by crossing Pioneer Hi-Bred International, Inc. proprietary inbred maize varieties. Methods for producing a maize plant that comprises crossing hybrid maize variety X13C704HR with another maize plant. Methods for producing a maize plant containing in its genetic material one or more traits introgressed into X13C704HR through backcross conversion and/or transformation, and to the maize seed, plant and plant part produced thereby. This invention relates to the maize variety X13C704HR, the seed, the plant produced from the seed, and variants, mutants, and minor modifications of maize variety X13C704HR. This invention further relates to methods for producing maize varieties derived from maize variety X13C704HR.