HIV, insulin resistance and type 2 diabetes mellitus (DM) are independently associated with cognitive impairment. Considering the synergistic effects of HIV and DM on cognition, these subjects are at increased risk of cognitive impairment. glucagon-like peptide 1 (GLP-1) receptors have wide tissue distribution including the central nervous system. The study hypothesis is that GLP-1 could potentially ameliorate the impairments in cognition in this population. This study will assess the impact of liraglutide on neurocognitive performance and peripheral inflammatory markers. It will also evaluate the effects of liraglutide on glycemic control and metabolic risk factors in HIV infected subjects with type 2 diabetes.