Polarization sensitivity is an intrinsic characteristic of the superconducting nanowire single-photon detector (SNSPD). It is caused by the periodical meander structure of the SNSPD, and may severely limit the scope of the SNSPD's applications. In this study, we have designed and fabricated a SNSPD with much reduced polarization sensitivity, based on a previously published theoretical result that involves high refractive index compensation materials. Using a home-built broadband automatic measurement system, the device detection efficiencies of the fabricated SNSPD have been measured for wavelengths ranging from 1200 to 1700 nm. The measurement results show that the polarization sensitivity of the fabricated device is greatly reduced, with the device detection efficiencies at 1550 nm being 61% and 56% for cases of parallel and perpendicular polarizations, respectively. The measurement results are in good agreement with the numerical simulations.