We present a sample of 10 low-mass active galactic nuclei (AGNs) selected from the 40-month NuSTAR serendipitous survey. The sample is selected to have robust NuSTAR detections at $3 - 24$~keV, to be at $z < 0.3$, and to have optical r-band magnitudes at least 0.5~mag fainter than an $L_star$ galaxy at its redshift. The median values of absolute magnitude, stellar mass and 2--10 X-ray luminosity of our sample are $langle M_rrangle = -20.03$, $langle M_starrangle = 4.6times10^{9}M_odot$, and $langle L_{2-10mathrm{keV}}rangle = 3.1times10^{42}$ erg s$^{-1}$, respectively. Five objects have detectable broad H$alpha$ emission in their optical spectra, indicating black-hole masses of $(1.1-10.4)times 10^6 M_odot$. We find that $30^{+17}_{-10}%$ of the galaxies in our sample do not show AGN-like optical narrow emission lines, and one of the ten galaxies in our sample, J115851+4243.2, shows evidence for heavy X-ray absorption. This result implies that a non-negligible fraction of low-mass galaxies might harbor accreting massive black holes that are missed by optical spectroscopic surveys and $<10$ keV X-ray surveys. The mid-IR colors of our sample also indicate these optically normal low-mass AGNs cannot be efficiently identified with typical AGN selection criteria based on WISE colors. While the hard ($>10$ keV) X-ray selected low-mass AGN sample size is still limited, our results show that sensitive NuSTAR observations are capable of probing faint hard X-ray emission originating from the nuclei of low-mass galaxies out to moderate redshift ($z<0.3$), thus providing a critical step in understanding AGN demographics in low-mass galaxies.
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