  In this paper, we present photometric and spectroscopic observations of a
subluminous type Ia supernova (SN Ia) 2012ij, which has an absolute $B$-band
peak magnitude $M_{B,\rm{max}}$ = $-$17.95 $\pm$ 0.15 mag. The $B$-band light
curve exhibits a fast post-peak decline with $\Delta m_{15}(B)$ = 1.86 $\pm$
0.05 mag. All the $R$ and $I$/$i$-band light curves show a weak secondary
peak/shoulder feature at about 3 weeks after the peak, like some transitional
subclass of SNe Ia, which could result from an incomplete merger of
near-infrared (NIR) double peaks. The spectra are characterized by Ti~{\sc ii}
and strong Si~{\sc ii} $\lambda$5972 absorption features that are usually seen
in low-luminosity objects like SN 1999by. The NIR spectrum before maximum light
reveals weak carbon absorption features, implying the existence of unburned
materials. We compare the observed properties of SN 2012ij with those predicted
by the sub-Chandrasekhar-mass and the Chandrasekhar-mass delayed-detonation
models, and find that both optical and NIR spectral properties can be explained
to some extent by these two models. By comparing the secondary maximum features
in $I$ and $i$ bands, we suggest that SN 2012ij is a transitional object
linking normal SNe Ia to typical 91bg-like ones. From the published sample of
SNe Ia from the $Carnegie~Supernova~Project~II$ (CSP-II), we estimate that the
fraction of SN 2012ij-like SNe Ia is not lower than $\sim$ 2%.
