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Polymer has been considered to be an ideal material option for integrated photonics devices. To measure these devices, normally the route of edge coupling is chosen to couple the light into or out of the polymer waveguide, which, however, demands a more difficult alignment procedure compared to the surface coupling. Due to the relatively low refractive indices of polymers, implementing the surface grating coupler for surface coupling in this material system remains a challenge. In this paper, we present a polymer-based surface grating coupler. Rather than through expensive complementary metal-oxide-semiconductor (CMOS) fabrication, the device is fabricated through a simple and fast UV-based soft imprint technique utilizing self-developed low-loss polymer material. The coupling efficiency is enhanced by embedding a thin Si3N4 layer between the waveguide core and under cladding layer. Around -19.8 dB insertion loss from single-mode fiber (SMF) to single-mode fiber is obtained for a straight waveguide with a grating coupler at each end. If the output light is collected with a multimode fiber, the insertion loss can be reduced to around -17.3 dB. Near 12% of the coupling efficiency is achieved between the polymer waveguide and SMF. The 3 dB bandwidth of the transmission is 32 nm and is centered at 1550 nm. The proposed surface grating coupler and its easy fabrication method would be very attractive for practical applications. [ABSTRACT FROM AUTHOR]