The purpose of this phase Ⅱ study is to assess the efficacy and safety of lenvatinib for anaplastic thyroid cancer patients who are diagnosed as unresectable. The total duration of the study will be 30 months. All patients will start administration of lenvatinib within 1 week of enrollment and receive the study drug 24mg orally once daily at almost the same time. 1 cycle consists of 4 weeks. Treatment term starts on the day 1st of drug administration of cycle 1 and administration will be continued until patients meet withdrawal criteria. Safety and efficacy assesment will be conducted on a regular basis during the trial. Tumor evaluation will be conducted at 4weeks, 8 weeks, 12 weeks, 16 weeks and at every 8 weeks after the 16th week since initial administration. When study drug administration terminated,tests of the drug termination will be conducted within 7 days of withdrawal and final observation will be conducted at 30 days after the last dose. Survival survey will be conducted at follow-up term. After the termination of the study drug, survival follow up survey will be conducted every 12 weeks unless patients withdraw enrollment of this study.

Inclusion Criteria:

1. Histologically confirmed as anaplastic thyroid cancer

2. Unresectable disease

3. Have measurable lesion defined by the RECIST version 1.1

4. Have adequate organ function and meet following laboratory value:

   1. Bone marrow function test within 14 days prior to enrollment:

      neutrophil count>=1.5 x 103/microL blood platelet count>=10.0 x 104/microL hemoglobin amount>=9.0 g/dL

   2. Liver function test within 14 days prior to enrollment:

      AST,ALT<=3.0 x ULN(without liver metastatic) AST,ALT<=5.0 x ULN(with liver metastatic) bilirubin<=2.0 mg/dL

   3. Kidney function test within 14 days prior to enrollment:

      GFR estimation>=50 ml/min/1.73 m2 GFR estimation calculated by following formula. Male:194 x(serum creatinine concentration)-1.094 x(Age)-0.287 Female:Male GFR estimation x 0.739

   4. Cardiac function test within 28 days prior to enrollment: 12-lead electrocardiogram: no clinically important abnormality as shown below: heart disease, severe arrhythmia etc.

5. Regardless of usage of antihypertensive drug, systolic blood pressure <=140 mm Hg and diastolic blood pressure <=90 mm Hg (If already taking antihypertensive drug, must have capacity of further antihypertensive therapy.)

6. ECOG performance status 0-2

7. Ability to swallow oral medications

8. Life expectancy greater than 8 weeks

9. Have signed written informed consent to participate in this study

Exclusion Criteria:

1. Have complications or medical history of

   1. Complication of brain metastasis (Exclude if cured and in clinically stable condition for more than 1 month prior to screening.)
   2. Treatment required complication of systemic infectious disease
   3. Complication of pulmonary fibrosis or interstitial pneumonitis
   4. Medical history of clinically significant cardiovascular disease within 6 months of initial dose as: NYHA class above 2 leveled congestive heart failure, unstable angina, cardiac infarction or cardiac arrhythmia with paroxysmal or required treatment e) Uncontrollable complication of diabetes mellitus f) hemoptysis within 3 weeks of enrollment (blood volume of more than half of teaspoon) g) Medical history of hemorrhagic or thrombotic disease within 6 months of enrollment h) If proteinuria values above 2+ by urinary protein qualitative test, conduct 24-hour urine collection and the urine protein determined as 1g/24 hours or more. (can substitute to the ratio of proteinuria in morning urine/creatinine) i) Malabsorption at gastrointestinal tract and any of the complication diseases that investigator considers that will be affected to lenvatinib absorption j) Recent major surgery within 2 weeks (if needle biopsy within 1 week) of enrollment k) Drainage required celomic fluid stagnation

2. Have history of lenvatinib administration

3. Confirmed tumor invasion to the carotid arteries

4. Have history of high dose external radiation therapy to cervical region, and irradiated tumor location close to the carotid arteries.

5. Have any unresolved toxicity greater than 1 by CTCAE v4.0.

6. Have active double cancer

7. Female patients who are pregnant, lactating, breast feeding or have childbearing potential

8. Psychiatric disorder and regarded by the investigator as inadequate for this study enrollment

9. Confirmed as no resistance to any component of this drug

10. Currently receiving other interventional clinical study treatment