We conducted simultaneous 22GHz water maser and 44GHz class I methanol maser surveys of newly-identified 282 H2 emission features from the $2.122{mu}m$ H2 narrowband image survey in the Galactic plane (UWISH2 project) using Korea VLBI Network (KVN) 21-m radio telescopes. We detected 16 and 13 new water and methanol maser sources, respectively. This result indicates that at least ~5% of the H2 emission features originate from young stellar objects (YSOs) that are in the right physical condition to produce the water and methanol masers. The masers are closely related to the current outflow activities in the Galactic plane. The power sources of these 23 diffused/collimated H2 emission features (six sources are detected for both masers) are likely to be intermediate-to high-mass YSOs, based on a comparison with the maser luminosities of other well-studied YSOs. Both maser velocities are mostly close to their own systemic velocities within 5 km/s, even though water masers generally show larger variabilities in the line intensities, velocities, and shapes than methanol masers. We also discovered three new water maser sources with high-velocity components: ~25 km/s red-shifted CMHO019, ~50 km/s blue-shifted CMHO132, and ~120 km/s blue-shifted CMHO182. In particular, we propose that the dominant blue-shifted water maser of CHMO182 could become a unique laboratory for the study of high-mass stellar jet and their accelerations.