This is a Phase 2b, open-label, non-randomized, single arm study to evaluate the safety, efficacy, and pharmacokinetics of HBI-8000 40 mg BIW in patients with relapsed or refractory PTCL (R/R PTCL). HBI 8000 will be administered orally approximately 30 minutes after any regular meal twice a week. There will be 3-4 days between dosing. A cycle is defined as consecutive 28 days. HBI-8000 administration will be continued until disease progression or unacceptable toxicities are observed despite appropriate dose reduction or treatment interruption.