We present results from simultaneous far-ultraviolet (FUV) and near-ultraviolet (NUV) observations of T Tauri stars (TTSs) in the Taurus molecular cloud with UVIT/AstroSat. This is the very first UVIT study of TTSs. From the spectral energy distribution of TTSs from FUV to IR, we show that classical TTSs (CTTSs) emit significantly higher UV excess compared to weak-line TTSs (WTTSs). The equivalent blackbody temperatures corresponding to the UV excess in CTTSs (>104 K) are also found to be relatively higher than those in WTTSs (<9250 K). From the UV excess, we have reclassified two WTTSs (BS Tau and V836 Tau) as CTTSs, which has been supported by the follow-up optical spectroscopic study using the Himalayan Chandra Telescope, showing strong Hα line emission. We find that CTTSs show strong excess emission in both the FUV (>107) and NUV (>103) bands, while WTTSs show strong excess only in the FUV (≲105), suggesting that excess emission in the NUV can be used as a tool to classify the TTSs. We also find a linear correlation between UV luminosity (a primary indicator of mass accretion) and Hα luminosity (a secondary indicator of mass accretion) with a slope of 1.20 ± 0.22 and intercept of 2.16 ± 0.70.