Abstract We present JCMT POL-2 850 μm dust polarization observations and Mimir H-band stellar polarization observations toward the starless core L 1512. We detect the highly ordered core-scale magnetic field traced by the POL-2 data, of which the field orientation is consistent with the parsec-scale magnetic fields traced by Planck data, suggesting the large-scale fields thread from the low-density region to the dense core region in this cloud. The surrounding magnetic field traced by the Mimir data shows a wider variation in the field orientation, suggesting there could be a transition of magnetic field morphology at the envelope-scale. L 1512 was suggested to be presumably older than 1.4 Myr in a previous study via time-dependent chemical analysis, hinting that the magnetic field could be strong enough to slow the collapse of L 1512. In this study, we use the Davis–Chandrasekhar–Fermi method to derive a plane-of-sky magnetic field strength (B _pos) of 18 ± 7 μG and an observed mass-to-flux ratio (λ _obs) of 3.5 ± 2.4, suggesting that L 1512 is magnetically supercritical. However, the absence of significant infall motion and the presence of an oscillating envelope are inconsistent with the magnetically supercritical condition. Using a virial analysis, we suggest the presence of a hitherto hidden line-of-sight magnetic field strength of ∼27 μG with a mass-to-flux ratio (λ _tot) of ∼1.6, in which case both magnetic and kinetic pressures are important in supporting the L 1512 core. On the other hand, L 1512 may have just reached supercriticality and will collapse at any time.