A novel maize variety designated X05A913 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 X05A913 with another maize plant. Methods for producing a maize plant containing in its genetic material one or more traits introgressed into X05A913 through backcross conversion and/or transformation, and to the maize seed, plant and plant part produced thereby. This invention relates to the maize variety X05A913, the seed, the plant produced from the seed, and variants, mutants, and minor modifications of maize variety X05A913. This invention further is relates to methods for producing maize varieties derived from maize variety X05A913.