The primary purpose of this study is to determine if sitagliptin (Januvia®) improves psoriasis severity after 24 weeks of treatment in 60 participants with psoriasis who do not have type 2 diabetes mellitus, and who are due to receive a course of narrowband ultraviolet-B phototherapy (NB-UVB). The investigators will compare the change in psoriasis severity in 60 participants treated with both sitagliptin and NB-UVB to 60 participants treated with NB-UVB alone. Participants will be recruited from two centres and after a 3 week run-in period will be followed prospectively for 36 weeks. Participants will be stratified by centre, plasma glycated haemoglobin level (HbA1c), obesity status and previous response to NB-UVB, after which they will be randomly allocated to Arm A or Arm B. Participants will be treated with either sitagliptin for 24 weeks and NB-UVB (Arm A), or NB-UVB alone (Arm B).