A novel maize variety designated 32D78 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 maize variety 32D78 with another maize plant. Methods for producing a maize plant containing in its genetic material one or more traits introgressed into 32D78 through backcross conversion and/or transformation, and to the maize seed, plant and plant part produced thereby. This invention relates to the maize variety 32D78, the seed, the plant produced from the seed, and variants, mutants, and minor modifications of maize variety 32D78. This invention further relates to methods for producing maize varieties derived from maize variety 32D78 and to the maize varieties derived by the use of those methods.