A novel maize variety designated X08M613 and seed, plants and plant parts thereof are produced by crossing inbred maize varieties. Methods for producing a maize plant by crossing hybrid maize variety X08M613 with another maize plant are disclosed. Methods for producing a maize plant containing in its genetic material one or more traits introgressed into X08M613 through backcrossing or genetic transformation, and to the maize seed, plant and plant part produced thereby are described. Maize variety X08M613, the seed, the plant produced from the seed, and variants, mutants, and minor modifications of maize variety X08M613 are provided. Methods for producing maize varieties derived from maize variety X08M613 and methods of using maize variety X08M613 are disclosed.