Cuproptosis is a new type of cell death that induces protein toxic stress and eventually leads to cell death. Hence, regulating cuproptosis in tumor cells is a new therapeutic approach. However, studies on cuproptosis-related long noncoding RNA (lncRNA) in head and neck squamous cell carcinoma (HNSC) have not been found. This study aimed to explore the cuproptosis-related lncRNAs prognostic marker and their relationship to immune microenvironment in HNSC by using bioinformatics methods. RNA sequencing, genomic mutations, and clinical data of TCGA_HNSC were downloaded from The Cancer Genome Atlas. HNSC patients were randomly assigned to either a training group or a validation cohort. The least absolute shrinkage and selection operator Cox regression and multivariate Cox regression models were used to determine the prognostic model in the training cohort, and its independent prognostic effect was further confirmed in the validation and entire cohorts. Based on previous literature, we collected 19 genes associated with cuproptosis. Afterward, 783 cuproptosis-related lncRNAs were obtained through coexpression. Cox model revealed and constructed eight cuproptosis-related lncRNAs prognostic marker (AL132800.1, AC090587.1, AC079160.1, AC011462.4, AL157888.1, GRHL3-AS1, SNHG16, and AC021148.2). Patients were divided into high- and low-risk groups based on the median risk score. The Kaplan-Meier survival curve revealed that the overall survival between the high- and low-risk groups was statistically significant. The receiver operating characteristic curve and principal component analysis demonstrated the accurate prognostic ability of the model. Univariate and multivariate Cox regression analysis showed that risk score was an independent prognostic factor. In addition, we used multivariate Cox regression to establish a nomogram of the predictive power of prognostic markers. The tumor mutation burden showed significant differences between the high- and low-risk groups. HNSC patients in the high-risk group responded better to immunotherapy than those in the low-risk group. We also found that risk scores were significantly associated with drug sensitivity in HNSC. In summary, our study identified eight cuprotosis-related lncRNAs signature of HNSC as the prognostic predictor, which may be promising biomarkers for predicting the benefit of HNSC immunotherapy as well as drug sensitivity.