We present photometric measurements of the short period variable star UY Cam, which has been classified as a delta Scuti or c-type RR Lyrae (RRc) variable in different catalogs. Based on the analyses on Fourier coefficients and (NUV - V)(0), we find that UY Cam is probably an RRc star. We obtain 58 new times of light maximum for UY Cam based on several sky surveys and our observations. Combining these with the times of light maximum in literature, a total of 154 times of light maximum are used to analyze the O - C diagram of UY Cam. The results show that the O - C pattern can be described by a downward parabolic component with a rate of -6.86 +/- 0.47 x 10(-11) dd(-1), and a cyclic variation with a period of 65.7 +/- 2.4 yr. We suppose these components are caused by the stellar evolution and the light travel time effect (LiTE) of a companion in elliptical orbit, respectively. By calculation, the minimum mass of the potential companion is about 0.17M(circle dot), and its mass should be less than or equal to the pulsation primary star when the inclination i > 22.degrees 5. Therefore, the companion should be a low-mass star, like a late-type main-sequence star or a white dwarf. Due to the unique property of UY Cam, we suggest that more observations and studies on UY Cam and other RRc stars are needed to check the nature of these stars, including the pulsations and binarities.