Abstract: We present a hard X-ray Nuclear Spectroscopic Telescope Array (NuSTAR) observation of PSR J0437-4715, the nearest millisecond pulsar. The known pulsations at the apparent pulse period approximately 5.76 ms are observed with a significance of 3.7sigma, at energies up to 20 keV above which the NuSTAR background dominates. We measure a photon index gamma = 1.50 +/- 0.25(90 per cent confidence) for the power-law fit to the non-thermal emission. It had been shown that spectral models with two or t…