We report observations of the Type Iax supernova (SN Iax) 2012Z at optical and near-infrared wavelengths from immediately after the explosion until $sim$ $260$ days after the maximum luminosity using the Optical and Infrared Synergetic Telescopes for Education and Research (OISTER) Target-of-Opportunity (ToO) program and the Subaru telescope. We found that the near-infrared (NIR) light curve evolutions and color evolutions are similar to those of SNe Iax 2005hk and 2008ha. The NIR absolute magnitudes ($M_{J}sim-18.1$ mag and $M_{H}sim-18.3$ mag) and the rate of decline of the light curve ($Delta$ $m_{15}$($B$)$=1.6 pm 0.1$ mag) are very similar to those of SN 2005hk ($M_{J}sim-17.7$ mag, $M_{H}sim$$-18.0$ mag, and $Delta$ $m_{15}$($B$)$sim1.6$ mag), yet differ significantly from SNe 2008ha and 2010ae ($M_{J}sim-14 - -15$ mag and $Delta$ $m_{15}$($B$)$sim2.4-2.7$ mag). The estimated rise time is $12.0 pm 3.0$ days, which is significantly shorter than that of SN 2005hk or any other Ia SNe. The rapid rise indicates that the $^{56}$Ni distribution may extend into the outer layer or that the effective opacity may be lower than that in normal SNe Ia. The late-phase spectrum exhibits broader emission lines than those of SN 2005hk by a factor of 6--8. Such high velocities of the emission lines indicate that the density profile of the inner ejecta extends more than that of SN 2005hk. We argue that the most favored explosion scenario is a `failed deflagration model, although the pulsational delayed detonations is not excluded.
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