Since chronic inflammation is associated with ovarian cancer growth and progression, some clinical studies have assessed the association between the pre-treatment neutrophil-to-lymphocyte ratio (NLR) and the prognosis of ovarian cancer. The purpose of this study was to assess the dynamic behavior of the NLR during the course of neoadjuvant chemotherapy (NACT) in patients with high grade serous (HGS) advanced epithelial ovarian cancer and assess its correlation with clinical response, progression free survival (PFS) and changes in other inflammatory indexes. We performed a prospective observational study on 161 patients who underwent NACT at the Department of Gynecologic Oncology, ARNAS G. Brotzu, Cagliari, between 2009 and 2019. NLR was evaluated before starting and after three cycles of NACT. Based on response after three cycles of NACT, patients were divided into two groups: responsive and non-responsive. The primary endpoint was to assess the predictive role of NLR by comparing the responsive and non-responsive patients at baseline and after three cycles of NACT. Secondary endpoints were (a) to correlate NLR with other inflammation markers (CRP, fibrinogen, ferritin, IL-6), albumin, and modified Glasgow Prognostic Score (mGPS) with NLR at baseline and after NACT; (b) to assess the association between NLR and PFS. We found that the NLR value at baseline was not associated with response to NACT, while a decrease in NLR after three cycles was correlated with a better response to NACT. Also, values of CRP, IL-6, ferritin, and mGPS after three cycles of NACT (but not at baseline) were significantly associated with clinical response. Moreover, we found that patients with a low NLR value after 3 cycles of NACT, but not at baseline, had a significantly higher PFS than patients with high NLR after 3 cycles of NACT. In conclusion, NLR change during treatment could serve as a predictive marker of response to NACT in patients with HGS advanced ovarian cancer. This allows for the early identification of non-responsive patients who will need treatment remodeling.