We report on the photometric observation of RZ LMi, which is a dwarf nova renowned for its extremely short ( 19 d) and regular supercycle, in 2013 and 2016. The supercycles observed in both years were longer than previously reported values of 19 d. Especially in 2016, we observed two exceptionally long superoutbursts with drations of 28 d and 48 d, which require very high mass transfer rate, 97 % and 99 % of the critical mass transfer rate, respectively. We consider thatthe object virtually experienced a transition to the nova-like state. We detected growing (stage A)superhumps with a mean period of 0.0602(1) d in 2013 and 2016, and possible negative super-humps with a period of 0.05710(1) d. By using the two periods, we estimated an orbital period of 0.05792 d. The orbital period suggests a mass ratio of 0.10, which is larger than mass ratios in WZ Sge-type dwarf novae with orbital periods similar to RZ LMi, and even above that of some ordinary SU UMa-type dwarf novae with similar orbital periods. The exceptionally high mass-transfer rate in this object may possibly be ecplained by a stripped secondary with an evolved core in a system evolving toward an AM CVn-type object.