The dust reverberation mapping is one of powerful methods to investigate the structure of the dusty tori in AGNs, and it has been performed on more than a hundred type 1 AGNs. However, no clear results have been reported on type 2 AGNs because their strong optical-UV extinction completely hides their accretion disc emission. Here we focus on an X-ray-bright type 2 AGN, NGC 2110, and utilize 2-20 keV X-ray variation monitored by MAXI to trace disc emission, instead of optical-UV variation. Comparing it with light curves in the WISE infrared (IR) W1 band ($lambda = 3.4$ $mu$m) and W2 band ($lambda = 4.6$ $mu$m) with cross-correlation analyses, we found candidates of the dust reverberation time lag at $sim60$ days, $sim130$ days, and $sim1250$ days between the X-ray flux variation and those of the IR bands. By examining the best-fitting X-ray and IR light curves with the derived time lags, we found that the time lag of $sim130$ days is most favoured. With this time lag, the relation between the time lag and luminosity of NGC 2110 is consistent with those in type 1 AGNs, suggesting that the dust reverberation in NGC 2110 mainly originates in hot dust in the torus innermost region, the same as in type 1 AGNs. As demonstrated by the present study, X-ray and IR simultaneous monitoring can be a promising tool to perform the dust reverberation mapping on type 2 AGNs.