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 ($S_mathrm{870mu m}>$ 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.
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