  We report detections of two 1.2 mm continuum sources ($S_\mathrm{1.2mm}$ ~
0.6 mJy) without any counterparts in the deep $H$- and/or $K$-band image (i.e.,
$K$-band magnitude $\gtrsim$ 26 mag). These near-infrared-dark faint millimeter
sources are uncovered by ASAGAO, a deep and wide-field ($\simeq$ 26 arcmin$^2$)
Atacama Large Millimeter/submillimeter Array (ALMA) 1.2 mm survey. One has a
red IRAC (3.6 and 4.5 $\mu$m) counterpart, and the other has been independently
detected at 850 and 870 $\mu$m using SCUBA2 and ALMA Band 7, respectively.
Their optical to radio spectral energy distributions indicate that they can lie
at $z \gtrsim$ 3-5 and can be in the early phase of massive galaxy formation.
Their contribution to the cosmic star formation rate density is estimated to be
~ 1 $\times$ 10$^{-3}$ $M_\odot$ yr$^{-1}$ Mpc$^{-3}$ if they lie somewhere in
the redshift range of $z$ ~ 3-5. This value can be consistent with, or greater
than that of bright submillimeter galaxies ($S_\mathrm{870\mu m}>$ 4.2 mJy) at
$z$ ~ 3-5. We also uncover 3 more candidates near-infrared-dark faint ALMA
sources without any counterparts ($S_\mathrm{1.2mm}$ ~ 0.45-0.86 mJy). These
results show that an unbiased ALMA survey can reveal the dust-obscured star
formation activities, which were missed in previous deep optical/near-infrared
surveys.
