A novel hybrid maize variety designated 34M78 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 34M78 with another maize plant. Methods for producing a maize plant containing in its genetic material one or more traits introgressed into 34M78 through backcross conversion and/or transformation, and to the maize seed, plant and plant part produced thereby. This invention relates to the maize hybrid variety 34M78, the hybrid seed, the hybrid plant produced from the seed, and variants, mutants, and minor modifications of hybrid maize variety 34M78. This invention further relates to methods for producing maize varieties derived from hybrid maize variety 34M78 and to the maize varieties derived by the use of those methods.