We present a sample of 10 low-mass active galactic nuclei (AGNs) selected from the 40-month Nuclear Spectroscopic Telescope Array (NuSTAR) serendipitous survey. The sample is selected to have robust NuSTAR detections at , to be at , and to have optical r-band magnitudes at least 0.5 mag fainter than an galaxy at its redshift. The median values of absolute magnitude, stellar mass, and 2-10 X-ray luminosity of our sample are , , and erg s−1, respectively. Five objects have detectable broad H emission in their optical spectra, indicating black hole masses of . We find that of the galaxies in our sample do not show AGN-like optical narrow emission lines, and one of the 10 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 X-ray surveys. The mid-IR colors of our sample also indicate that these optically normal low-mass AGNs cannot be efficiently identified with typical AGN selection criteria based on Wide Field Infrared Survey Explorer colors. While the hard ( 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 ( ), thus providing a critical step in understanding AGN demographics in low-mass galaxies.