To provide the census of the sources contributing to the X-ray background peak above 10 keV, NuSTAR is performing extragalactic surveys using a three-tier wedding cake approach. We present the NuSTAR survey of the COSMOS field, the medium sensitivity and medium area tier, covering 1.7 deg2 and overlapping with both Chandra and XMM-Newton data. This survey consists of 121 observations for a total exposure of ~3 Ms. To fully exploit these data, we developed a new detection strategy, carefully tested through extensive simulations. The survey sensitivity at 20% completeness is 5.9, 2.9 and 6.4 x 10^-14 erg/cm2/s in the 3-24 keV, 3-8 keV and 8-24 keV bands, respectively. By combining detections in 3 bands, we have a sample of 91 NuSTAR sources with 10^42 -10^45.5 erg/s luminosities and redshift z=0.04-2.5. Thirty two sources are detected in the 8-24 keV band with fluxes ~100 times fainter than sources detected by Swift-BAT. Of the 91 detections, all but four are associated with a Chandra and/or XMM-Newton point-like counterpart. One source is associated with an extended lower energy X-ray source. We present the X-ray (hardness ratio and luminosity) and optical-to-X-ray properties. The observed fraction of candidate Compton-thick AGN measured from the hardness ratio is between 13-20%. We discuss the spectral properties of NuSTAR J100259+0220.6 (ID 330) at z=0.044, with the highest hardness ratio in the entire sample. The measured column density exceeds 10^24 /cm2, implying the source is Compton-thick. This source was not previously recognized as such without the >10 keV data.
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