A CCD photometry of the dwarf nova MASTER OT J172758.09 +380021.5 was carried out in 2019 during 134 nights. Observations covered three superoutbursts, five normal outbursts and quiescence between them. The available ASASSN and ZTF data for 2014 – 2020 were also examined. Spectral observations were done in 2020 when the object was in quiescence. Spectra and photometry revealed that the star is an H-rich active ER UMa-type dwarf nova with a highly variable supercycle (time interval between two successive superoutbursts) of ∼ 50 – 100 d that implies a high and variable mass-transfer rate. MASTER OT J172758.09+380021.5 demonstrated peculiar behaviour: short-lasted superoutbursts (a week); a slow superoutburst decline and cases of rebrightenings; low frequency (from none to a few) of the normal outbursts during the supercycle. In 2019 a mean period of positive superhumps was found to be 0.05829 d during the superoutbursts. Late superhumps with a mean period of 0.057915 d which lasted about ∼ 20 d after the end of superoutburst and were replaced by an orbital period of 0.057026 d or its orbital-negative superhump beat period were detected. An absence of eclipse in the orbital light curve and its moderate amplitude are consistent with the orbital inclination of about 40° found from spectroscopy. The blue peaks of the V-Ic and B-Rc colour indices of superhumps during the superoutburst coincided with minima of the light curves, while B-Rc of the late superhumps coincided with a rising branch of the light curves. We found that a low mass ratio q = 0.08 could explain most of the peculiarities of MASTER OT J172758.09+380021.5. The mass-transfer rate should be accordingly higher than what is expected from gravitational radiation only, this assumes the object is in a post-nova state and underwent a nova eruption relatively recently – hundreds of years ago. This object would provide probably the first observational evidence that a nova eruption can occur even in CVs near the period minimum