We report the multiferroic properties of 12R-type hexagonal Ba(Ti1/3Mn2/3)O3-δ found in Mn-doped BaTiO3 series samples. Hysteresis measurements reveal the coexistence of weak ferromagnetism and ferroelectricity at room temperature. Furthermore, frequency-driven dynamic ferroelectric phase transition is disclosed around a critical frequency of 220 Hz. Analyses on the dielectric relaxation, leakage current, crystal structure, and magnetic susceptibility lead us to conclude that the response of polarons dominates the observed physical properties, and the dynamic phase transition may ascribe to the response mode changes of the localized electrons. More importantly, we figure out the crucial factors leading to difference of the ferroelectric and magnetic properties of the 12R-type Ba(Ti1/3Mn2/3)O3-δ samples from that of the 6H-type Ba(Ti1-xMx)O3-δ (M = Fe, Mn) samples.