We present a broadband (0.4–70 keV) X-ray spectral analysis of the luminous infrared galaxy (LIRG) system Mrk 463 observed with Nuclear Spectroscopic Telescope Array (NuSTAR), Chandra, and XMM-Newton, which contains double active galactic nuclei (AGNs; Mrk 463E and Mrk 463W) with a separation of ~3.8 kpc. Detecting their transmitted hard X-ray >10 keV continua with NuSTAR, we confirm that Mrk 463E and Mrk 463W have AGNs with intrinsic luminosities of (1.6–2.2) × 10^(43) and (0.5–0.6) × 10^(43) erg s^(−1) (2–10 keV) obscured by hydrogen column densities of 8 × 10^(23) and 3 × 10^(23) cm^(−2), respectively. Both nuclei show strong reflection components from cold matter. The luminosity ratio between X-ray (2–10 keV) and [O IV] 25.89 μm of Mrk 463E is ~5 times smaller than those of normal Seyfert galaxies, suggesting that the intrinsic SED is X-ray weak relative to the UV luminosity. In fact, the bolometric AGN luminosity of Mrk 463E estimated from L'-band (3.8 μm), [O IV] 25.89 μm, and [Ne V] 14.32 μm lines indicate a large bolometric-to-X-ray luminosity ratio, κ_(2–10 keV) ≈ 110–410, and a high Eddington ratio, λ_(Edd) ~ 0.4–0.8. We suggest that the merger triggered a rapid growth of the black hole in Mrk 463E, which is not yet deeply "buried" by circumnuclear dust. By contrast, the L'-band luminosity of Mrk 463W is unusually small relative to the X-ray luminosity, suggesting that the Eddington ratio is low (<10^(−3)) and it might be still in an early phase of merger-driven AGN activity