This is a phase II study of an investigational drug, Axitinib following prior antiangiogenic therapy in patients with advanced hepatocellular carcinoma. Hepatocellular carcinoma (HCC) is a primary cancer of the liver. Angiogenesis is a physiological process involving the growth of new blood vessels from pre-existing vessels. A tyrosine kinase is an enzyme that can inhibit angiogenesis. In this study, patients with advanced HCC who have failed prior antiangiogenic therapy, will receive Axitinib in cycles of 4 weeks. Axitinib is an oral, potent and selective inhibitor of angiogenesis. This study will evaluate the response rate of HCC following treatment with Axitinib as well as safety, feasibility, overall survival of patients, progression-free survival, and quality of life in persons with unresectable HCC. The study also compares response determined by RECIST to response determined by Choi Criteria.