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Utilizing \textit{Chandra}, \textit{XMM-Newton} and \textit{NuSTAR}, a wide-band X-ray spectrum through 0.2 to 20 keV is reported from the western hot spot of Pictor A. In particular, the X-ray emission is significantly detected in the 3 to 20 keV band at 30 sigma by \textit{NuSTAR}. This is the first detection of hard X-rays with energies above 10 keV from a jet termination hot spot of active galactic nuclei. The hard X-ray spectrum is well described with a power-law model with a photon index of $\mathitΓ=1.8\pm0.2$, and the flux is obtained to be $(4.5\pm0.4)\times10^{-13}$ erg s$^{-1}$ cm$^{-2}$ in the 3 to 20 keV band. The obtained spectrum is smoothly connected with those soft X-ray spectra observed by \textit{Chandra} and \textit{XMM-Newton}. The wide-band spectrum shows a single power-law spectrum with a photon index of $\mathitΓ=2.07\pm0.03$, excluding any cut-off/break features. Assuming the X-rays as synchrotron radiation of the electrons, the energy index of the electrons is estimated as $p=2\mathitΓ-1=3.14\pm0.06$ from the wide-band spectrum. Given that the X-ray synchrotron emitting electrons quickly lose their initial energies via synchrotron radiation, the energy index of electrons at acceleration sites is estimated as $p_\mathrm{acc}=p-1=2.14\pm0.06$. This is consistent with the prediction of the diffusive shock acceleration. Since the spectrum has no cut-off feature up to 20 keV, the maximum electron energy is estimated to be no less than 40 TeV.