Low-current　measurement　is　a　challenging　task　for　polarimetric　fiber-optic　current-sensing　(FOCS)　systems　due　to　low　signal-to-noise　ratio　(SNR)　and　sensitivity　to　current　(STC).　To　tackle　the　challenges,　this　article　proposes　a　FOCS　approach　on　bias-added　measurement　and　main-component　reconstruction.　To　enhance　STC,　the　adopted　FOCS　structure　is　based　on　bias-added　measurement　using　a　bias-current　coil　and　a　single-axis　working　circulator　instead　of　traditional　polarizers.　However,　the　unavoidable　noise　would　decrease　the　SNR　of　FOCS　output.　An　algorithm　of　main-component　reconstruction　is　presented　to　filter　out　the　noise.　The　main-component　distribution　of　the　FOCS　output　is　analyzed　by　a　feature　vector　based　on　the　spectral　subzones.　Using　an　appropriate　threshold,　the　subzones　with　prominent　features　are　self-adaptively　decomposed　to　extract　the　main　components　by　fast　matrix　decomposition.　At　last,　the　main　components　are　adopted　to　reconstruct　the　FOCS　signal.　In　comparison　with　other　reflective　methods,　the　experimental　data　suggest　that　the　STC　and　SNR　of　the　proposed　approach　can　be　increased　by　200%　and　22%,　respectively.　The　similarity　between　the　expected　and　reconstructed　signals　reaches　0.9993　under　the　premise　of　a　small　measurement　error.