The Na+/H+ exchangers (NHXs) are a class of transporters involved in ion balance during plant growth and abiotic stress. We performed systematic bioinformatic identification and expression-characteristic analysis of CaNHX genes in pepper to provide a theoretical basis for pepper breeding and practical production. At the whole-genome level, the members of the CaNHX gene family of cultivated and wild pepper were systematically identified using bioinformatics methods. Sequence alignment and phylogenetic tree construction were performed using MEGA X software, and the gene functional domain, conserved motif, and gene structure were analyzed and visualized. At the same time, the co-expression network of CaNHX genes was analyzed, and salt-stress analysis and fluorescence quantitative verification of the Zunla-1 cultivar under stress conditions were performed. A total of 9 CaNHX genes were identified, which have typical functional domains of the Na+/H+ exchanger gene. The physical and chemical properties of the protein showed that the protein was hydrophilic, with a size of 503–1146 amino acids. Analysis of the gene structure showed that Chr08 was the most localized chromosome, with 8–24 exons. Cis-acting element analysis showed that it mainly contains cis-acting elements such as light response, salicylic acid response, defense, and stress response. Transcriptom and co-expression network analysis showed that under stress, the co-expressed genes of CaNHX genes in roots and leaves were more obvious than those in the control group, including ABA, IAA, and salt. The transcriptome and co-expression were verified by qRT-PCR. In this study, the CaNHX genes were identified at the genome level of pepper, which provides a theoretical foundation for improving the stress resistance, production, development, and utilization of pepper in genetic breeding.