The twin Sentinel-1 (S1) satellites have been extensively acquiring synthetic aperture radar (SAR) data in the Arctic, providing the unique opportunity to obtain ocean dynamic parameters with both high spatial resolution and wide swath coverage in the marginal ice zone (MIZ). In this paper, we proposed a method for retrieving the ocean significant wave height (SWH) from S1 SAR data in horizontal-horizontal (HH) polarization based on a backpropagation neural network (BPNN). A total of 4,273 scenes from S1 extra wide swath mode data acquired in the Arctic were collocated with data from four radar altimeters (RA), yielding 126,128 collocated data pairs. These data were separated into training and testing datasets to develop a BPNN model for retrieving SWH. Comparing the S1 retrieved SWH using the testing dataset with the RA SWH yielded a bias of 0.17 m, a root-mean-square error of 0.71 m and a scatter index of 23.05% for SWH less than 10 m. The S1 retrieved SWH were further compared with CFOSAT/SWIM data acquired in the Arctic between August 2019 and May 2020 to validate the SWIM performance on wave measurements at different beams.