We present near-infrared polarimetric results for the N159/N160 star-forming complex in the Large Magellanic Cloud with SIRPOL, the polarimeter of the Infrared Survey Facility. We separated foreground sources using their visual extinction derived from near-infrared photometric data. The 45 young stellar candidates and 2 high-excitation blobs were matched with our sources, and 12 of them showed high polarization that did not originate from the interstellar dust. We made a polarimetric catalog of 252, 277, and 89 sources at the J, H, and K_s_ bands, respectively. Based on the ratios of the polarization degree between these bands, we verify that the origin of these polarized sources is the dichroic extinction from the interstellar dust aligned by the magnetic field and that the ratios follow a power-law dependence of P_{lambda}_~{lambda}^-0.9^. The linear polarization vectors projected onto the H{alpha} image of the complex turned out to follow the local magnetic field structure. The vector map overlaid on dust and gas emissions shows the close correlation between the magnetic field structure and surrounding interstellar medium. We suggest that the derived magnetic field structure supports the sequential formation scenario of the complex.