The HH 1-2 region in the L1641 molecular cloud was observed in the near-infrared (IR) J, H, and K_s bands, and imaging polarimetry was performed. Seventy-six point-like sources were detected in all three bands. The near-IR polarizations of these sources seem to be caused mostly by the dichroic extinction. Using a color-color diagram, reddened sources with little IR excess were selected to trace the magnetic field structure of the molecular cloud. The mean polarization position angle of these sources is about 111°, which is interpreted as the projected direction of the magnetic field in the observed region of the cloud. The distribution of the polarization angle has a dispersion of about 11°, which is smaller than what was measured in previous studies. This small dispersion gives a rough estimate of the strength of the magnetic field to be about 130 μG and suggests that the global magnetic field in this region is quite regular and straight. In contrast, the outflows driven by young stellar objects in this region seem to have no preferred orientation. This discrepancy suggests that the magnetic field in the L1641 molecular cloud does not dictate the orientation of the protostars forming inside.