Authors:Fukui et alAbstract:We report the first ground-based transit observation of K2-3d, a 1.5 R_Earth planet supposedly within the habitable zone around a bright M-dwarf host star, using the Okayama 188-cm telescope and the multi(grz)-band imager MuSCAT. Although the depth of the transit (0.7 mmag) is smaller than the photometric precisions (1.2, 0.9, and 1.2 mmag per 60 s for g, r, and z bands, respectively), we marginally but consistently identify the transit signal in all three bands, by taking advantage of the transit parameters from K2, and by introducing a novel technique that leverages multi-band information to reduce the systematics caused by second-order extinction. We also revisit previously analyzed Spitzer transit observations of K2-3d to investigate the possibility of systematic offsets in transit timing, and find that all the timing data can be explained well by a linear ephemeris. We revise the orbital period of K2-3d to be 44.55612 \pm 0.00021 days, which corrects the predicted transit times in 2019, i.e., the JWST era, by \sim80 minutes. Our observation demonstrates that (1) even ground-based, 2-m class telescopes can play an important role in refining the transit ephemeris of small-sized, long-period planets, and that (2) a multi-band imager is useful to reduce the systematics of atmospheric origin, in particular for bluer bands and for observations conducted at low-altitude observatories.