We present the results of simultaneous 450 μm and 850 μm polarization observations toward the massive starforming region NGC 2071IR, a target of the BISTRO (B-fields in STar-forming Region Observations) Survey, using the POL-2 polarimeter and SCUBA-2 camera mounted on the James Clerk Maxwell Telescope. We find a pinched magnetic field morphology in the central dense core region, which could be due to a rotating toroidal disklike structure and a bipolar outflow originating from the central young stellar object IRS 3. Using the modified Davis-Chandrasekhar-Fermi method, we obtain a plane-of-sky magnetic field strength of 563 ± 421 μG in the central ∼0.12 pc region from 850 μm polarization data. The corresponding magnetic energy density of 2.04 × 10 −8 erg cm −3 is comparable to the turbulent and gravitational energy densities in the region. We find that 85 NAOJ Fellow.