According to the invention, there is provided a hybrid maize plant, designated as 33H05, produced by crossing two Pioneer Hi-Bred International, Inc. proprietary inbred maize lines. This invention relates to the hybrid seed 33H05, the hybrid plant produced from the seed, and variants, mutants, and trivial modifications of hybrid 33H05. This invention also relates to methods for producing a maize plant containing in its genetic material one or more transgenes and to the transgenic maize plants produced by those methods. This invention further relates to methods for producing maize lines derived from hybrid maize line 33H05 and to the maize lines derived by the use of those methods.