The near-contact binary UU Lyn with an F3V-type primary was observed in 2005 and 2006. With the latest version of the Wilson-Devinney code, the photometric elements were computed. The results reveal that UU Lyn is a marginal contact system with a large temperature difference of about 1900 K between the primary and secondary components. All available eclipse times, including new ones, were used in the analysis. The results show that the orbital period of this system undergoes a continuous decrease at a rate of dP/dt ≤ -1.84×10-8 d yr-1. With the period decrease, UU Lyn may evolve from the present short-period marginal contact system into a contact system with true thermal contact. This target might just be undergoing the cycles predicted by the theory of thermal relaxation oscillations (TRO). It is an interesting example resembling BL And, GW Tau, ZZ Aur, KQ Gem, CN And and AD Cnc, that lie in the key evolutionary stage.