 Diabetes is a significant cause of cardiovascular and cerebrovascular events. Especially, diabetic patients with cardiovascular risk factors were significantly higher risk for cardiovascular and cerebrovasculara event. Therefore, several medical management strategies including anti-diabetic medications and statins were considered for those patients. However, in spite of such treatment, still many patients have cardiovascular and cerebrovascular events. One of the hypothesis is the residual risk such as elevated low-density lipoprotein cholesterol LDLC even with statin therapy. Anagliptin, one of the dipeptidyl peptidase-4 DPP4 inhibiors, was reported to reduce LDLC and may have pontential to decrease the cardiovascular and cerebrovascular risk for such patients on statins. We, thus, conduct a randomized controlled trial to compare Anagliptin or Sitagliptin in terms of change of LDLC for 52 weeks as well as glycemic control. 