  We report on NuSTAR observations of the mixed morphology supernova remnant
(SNR) W49B, focusing on its nonthermal emission. Whereas radio observations as
well as recent gamma-ray observations evidenced particle acceleration in this
SNR, nonthermal X-ray emission has not been reported so far. With the
unprecedented sensitivity of NuSTAR in the hard X-ray band, we detect a
significant power-law-like component extending up to $\sim 20~{\rm keV}$, most
probably of nonthermal origin. The newly discovered component has a photon
index of $\Gamma =1.4^{+1.0}_{-1.1}$ with an energy flux between 10 and 20 keV
of $(3.3 \pm 0.7) \times 10^{-13}~{\rm erg}~{\rm cm}^{-2}~{\rm s}^{-1}$. The
emission mechanism is discussed based on the NuSTAR data combined with those in
other wavelengths in the literature. The NuSTAR data, in terms both of the
spectral slope and of the flux, are best interpreted as nonthermal electron
bremsstrahlung. If this scenario is the case, then the NuSTAR emission provides
a new probe to sub-relativistic particles accelerated in the SNR.
