AP2 (APETALA2)/EREBP (ethylene-responsive element-binding protein), cytochrome c oxidase (COX) and nonspecific lipid transfer proteins (LTP) play important roles in the response to drought stress. This is the first study to identify the COX gene in Zea mays L. via genome-wide analysis. The qRT‒PCR results indicated that AP2/EREBP, COX and LTP were downregulated, with fold changes of 0.84, 0.53 and 0.31, respectively, after 12 h of drought stress. Genome-wide analysis identified 78 AP2/EREBP, 6 COX and 10 LTP genes in Z. mays L. Domain analysis confirmed the presence of the AP2 domain, Cyt_c_Oxidase_Vb domain and nsLTP1 in the AP2/EREBP, COX and LTP proteins, respectively. The AP2/EREBP protein family (AP2) includes five different domain types: the AP2/ERF domain, the EREBP-like factor (EREBP), the ethylene responsive factor (ERF), the dehydration responsive element binding protein (DREB) and the SHN SHINE. Synteny analysis of the AP2/EREBP, COX and LTP genes revealed collinearity orthologous relationships in O. sativa, H. vulgare and A. thaliana. AP2/EREBP genes were found on the 10 chromosomes of Z. mays L. COX genes were found on chromosomes 1, 3, 4, 5, 7 and 8. LTP genes were found on chromosomes 1, 3, 6, 8, 9 and 10. In the present study, the Ka/Ks ratios of the AP2/EREBP paralogous pairs indicated that the AP2/EREBP genes were influenced primarily by purifying selection, which indicated that the AP2/EREBP genes received strong environmental pressure during evolution. The Ka/Ks ratios of the COX-3/COX-4 paralogous pairs indicate that the COX-3/COX-4 genes were influenced primarily by Darwinian selection (driving change). For the LTP genes, the Ka/Ks ratios of the LTP-1/LTP-10, LTP-5/LTP-3 and LTP-4/LTP-8 paralogous pairs indicate that these genes were influenced primarily by purifying selection, while the Ka/Ks ratios of the LTP-2/LTP-6 paralogous pairs indicate that these genes were influenced primarily by Darwinian selection. The duplication time of the AP2/EREBP paralogous gene pairs in Z. mays L. ranged from approximately 9.364 to 100.935 Mya. The duplication time of the COX-3/COX-4 paralogous gene pair was approximately 5.217 Mya. The duplication time of the LTP paralogous gene pairs ranged from approximately 19.064 to 96.477 Mya. The major focus of research is to identify the genes that are responsible for drought stress tolerance to improve maize for drought stress tolerance. The results of the present study will improve the understanding of the functions of the AP2/EREBP, COX and LTP genes in response to drought stress.