In this work we conduct a thorough investigation of the X-ray and ultraviolet (UV) properties of Y Gem based on six archival XMM-Newton and Chandra observations to explore the nature of the system. The results show that Y Gem has strong (1032-34 erg s-1) X-ray emission, including a hard (with a maximum emission temperature of 8-16 keV) and a soft (with emission temperatures of 0.02-0.2 and 0.2-0.9 keV) component. The integrated UV luminosity of Y Gem reaches ~1035 erg s-1. We show that the previous asymptotic giant branch-main-sequence (AGB-MS) Roche-lobe overflow (RLOF) scenario is dynamically unstable and can hardly explain the ~10 keV X-ray emission temperature. We propose Y Gem as a symbiotic star, where a white dwarf (WD) accretes from its AGB companion based on its X-ray and UV properties. We make numerical simulations to examine the evolutionary history of this system. The simulations can produce the observed properties of Y Gem in the wind WRLOF scenario. An ~0.8M ⊙ WD with a ~1.0-1.8M ⊙ companion in a ~2000-32,000 day initial orbit may evolve to a Y Gem-like system. Our finding implies a potential population of symbiotic stars that may have been misclassified as AGB-MS binaries. What is more, their high mass accretion rates may enable mass accumulation to the WD and makes them candidates of Type Ia supernovae progenitors.