Background and Objectives: For stage IIIb–IV ovarian cancer, bevacizumab-containing treatment is considered the standard of care. The purpose of this study was to evaluate the efficacy of bevacizumab in combination with carboplatin and paclitaxel as a first-line treatment for advanced ovarian cancer. Materials and Methods: Eligible patients had stage IIIc–IV ovarian cancer according to the International Federation of Gynecology and Obstetrics with no clinical signs or symptoms of gastrointestinal obstruction or a history of abdominal fistulae, gastrointestinal perforation, or intra-abdominal abscess or evidence of rectosigmoid involvement by pelvic examination, bowel involvement on computed tomography, or clinical symptoms of bowel obstruction in the previous 6 months. After debulking surgery, the patients received 175 mg/m² paclitaxel and carboplatin (AUC 6) for the first six cycles and 7.5 mg/kg bevacizumab every three weeks up to 17 cycles until disease progression, unacceptable toxicity, or consent withdrawal. The primary endpoint was progression-free survival. The secondary endpoint was overall survival. Results: Between April 2017 and March 2020, 35 patients began study treatment. Bevacizumab was administered at 7.5 mg/kg in all the patients and for more than 7.5 months in 70% of them. The median progression-free survival was 20 months (95% CI: 16–23). The median overall survival was not reached. Conclusions: This was, to our knowledge, the first trial in Serbia to show progression-free survival and overall survival of combination regimens in advanced ovarian cancer. Based on the observed progression-free survival, bevacizumab combined with chemotherapy should be considered as a standard option in advanced ovarian cancer.