We present new BVRI light curves of UY UMa with no O’Connell effect and a flat bottom secondary eclipse. Light curve synthesis with the Wilson-Devinney code gives a new solution, which is quite different from the previous study: UY UMa is an A-subtype over-contact binary with a small mass ratio of q = 0.21, a high inclination of 81˚.4, a small temperature difference of ΔT = 18˚, a large fill-out factor of f = 0.61, and a third light of approximately 10% of the total systemic light. The absolute dimensions were newly determined. Seventeen new times of minimum light have been calculated from our observations. The period study indicates that the orbital period has intricately varied in a secular period increase in which two cyclical terms with periods of 12y.0 and 46y.3 are superposed. The secular period increase was interpreted to be due to a conservative mass transfer of 2.68 × 10–8 M⊙/yr from the less massive to the more massive star. The cyclical components are discussed in terms of double-light time contributions from two additional bound stars. The statistical relations of Yang & Qian (2015) among the physical parameters of 45 deep, low mass ratio contact binaries were revisited by using the physical parameters of UY UMa and 25 Kepler contact binaries provided by Şenavci et al. (2016).