UWISH2 (UKIRT Widefield Infrared Survey for $H_2$) is an unbiased, narrow-band imaging survey of the Galactic plane in the $H_2$ 1-0 S(1) emission line at $2.122{mu}m$ using the Wide-Field Camera (WFCAM) at the United Kingdom Infrared Telescope (UKIRT). The survey covers about 150 square degrees of the first Galactic quadrant ($10^{circ}$ < l < $65^{circ}$; $-1.3^{circ}$ < b < $+1.3^{circ}$). The images have a $5{sigma}$ detection limit of point sources of K~18 mag and the surface brightness limit is $10^{-19};W;m^{-2}$ $arcsec^{-2}$. The survey operation began on 28 July 2009 and has completed on 17 August 2011. We have been studying the supernova remnants (SNRs) in the UWISH2 survey area. Among the known 274 Galactic SNRs, the survey area includes 65 SNRs or 24 percent of the known SNRs. The wide-field and high-quality UWISH2 images allow us to identify both the diffuse extended and compact $H_2$ emission associated with SNRs, which is useful for understanding their physical environment and evolution. The continuum is subtracted from the narrow-band $H_2$ images using the K-band continuum images obtained as part of the UKIDSS GPS (UKIRT Infrared Deep Sky Survey of the Galactic Plane). So far, we have inspected 42 SNRs, and found distinct H2 emission in 14 SNRs. The detection rate is 33%. Some of the SNRs show bright, complex, and interesting structures that have never been reported in previous studies. In this report, we present our identification scheme and preliminary results.