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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 $Δm_{15}(B)$ = 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} $λ$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%.