  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.
