The soft \gamma -ray repeater ( SGR ) 0526–66 is the first-identified magnetar , and is projected within the supernova remnant N49 in the Large Magellanic Cloud . Based on our \sim 50 ks NuSTAR observation , we detect the quiescent-state 0526–66 for the first time in the 10–40 keV band . Based on the joint analysis of our NuSTAR and the archival Chandra ACIS data , we firmly establish the presence of the nonthermal component in the X-ray spectrum of 0526–66 in addition to the thermal emission . In the best-fit blackbody ( BB ) plus power law ( PL ) model , the slope of the PL component ( photon index \Gamma = 2.1 ) is steeper than those ( \Gamma \mathrel { \hbox { \hbox to 0.0 pt { \hbox { \lower 4.0 pt \hbox { $ \sim$ } } } \hbox { $ < $ } } } 1.5 ) for other magnetars . The soft part of the X-ray spectrum can be described with a BB component with the temperature of kT = 0.43 keV . The best-fit radius ( R = 6.5 km ) of the X-ray-emitting area is smaller than the canonical size of a neutron star . If we assume an underlying cool BB component with the canonical radius of R = 10 km for the neutron star in addition to the hot BB component ( 2BB + PL model ) , a lower BB temperature of kT = 0.24 keV is obtained for the passively cooling neutron star ’ s surface , while the hot spot emission with kT = 0.46 keV dominates the thermal spectrum ( \sim 85 % of the thermal luminosity in the 0.5–5 keV band ) . The nonthermal component ( \Gamma \sim 1.8 ) is still required .