Lung adenocarcinoma (LUAD) is a commonly occurring histological subtype of lung cancer. Glutathione peroxidase 4 (GPX4) is an important regulatory factor of ferroptosis and is involved in the development of many cancers, but its prognostic significance has not been systematically described in LUAD. In this study, we focused on developing a robust GPX4-related prognostic signature (GPS) for LUAD. Data for the training cohort was extracted from The Cancer Genome Atlas, and that for the validation cohort was sourced from the GSE72094 dataset including 863 LUAD patients. GPX4-related genes were screened out by weighted gene coexpression network analysis and Spearman’s correlation analysis. Then, Cox regression and least absolute shrinkage and selection operator regression analyses were employed to construct a GPS. The ESTIMATE algorithm, single-sample gene set enrichment analysis (ssGSEA), and GSEA were utilized to evaluate the relationship between GPS and the tumor microenvironment (TME). We constructed and validated a GPS premised on four GPX4-related genes (KIF14, LATS2, PRKCE, and TM6SF1), which could classify LUAD patients into low- and high-score cohorts. The high-risk cohort presented noticeably poorer overall survival (OS) as opposed to the low-risk cohort, meaning that the GPS may be utilized as an independent predictor of the OS of LUAD. The GPS was also adversely correlated with multiple tumor-infiltrating immune cells and immune-related processes and pathways in TME. Furthermore, greater sensitivity to erlotinib and lapatinib were identified in the low-risk cohort based on the GDSC database. Our findings suggest that the GPS can effectively forecast the prognosis of LUAD patients and may possibly regulate the TME of LUAD.