Ovarian cancer is a kind of gynecological malignancy with high mortality. Ferroptosis is a new type of iron-dependent cell death characterized by the formation of lipid peroxides and excessive accumulation of reactive oxygen species. Studies have shown that ferroptosis modulates tumor genesis, progression, and invasion, including ovarian cancer. Based on the mRNA expression data from TCGA, we construct a scoring system using consensus clustering analysis, univariate Cox regression analysis, and least absolute selection operator. Then, we systematically evaluate the relationship between score and clinical characteristics of ovarian cancer. The result from the prediction of biofunction pathways shows that score serves as an independent prognostic marker for ovarian cancer and affects tumor progression by modulating tumor metastasis. Moreover, immunocytes such as activated CD4 T cell, activated CD8 T cell, regulatory T cells, macrophage, and stromal cells, including adipocytes, epithelial cells, and fibroblast infiltrate more in the tumor microenvironment in a high-score group, indicating ferroptosis can also affect tumor immune landscape. Critically, four potentially sensitive drugs, including staurosporine, epothilone B, DMOG, and HG6-64-1 based on the scores, are predicted, and DMOG is recognized as a novel targeted drug for ovarian cancer. In general, we construct the scoring system based on ferroptosis-related genes that can predict the prognosis of ovarian cancer patients and propose that ferroptosis may affect ovarian cancer progression by mediating tumor metastasis and immune landscape. Novel drugs to target ovarian cancer are also predicted.