The structural phase transition in hexagonal BaMnO3 occurring at TC=130 K was studied in ceramic samples using electron and X-ray diffraction, second harmonic generation as well as by dielectric and lattice dynamic spectroscopies. The low-temperature phase (space group P 63cm) is ferroelectric with a triplicated unit cell. The phase transition is driven by an optical soft mode from the Brillouin-zone boundary [q = ( , 0)]; this mode activates in infrared and Raman spectra below TC and it hardens according to the Cochran law. Upon cooling below TC, the permittivity exhibits an unusual linear increase with temperature; below 60 K, in turn, a frequency-dependent decrease is observed, which can be explained by slowing-down of ferroelectric domain wall motions. Based on our data we could not distinguish whether the high-temperature phase is paraelectric or polar (space groups P 63/mmc or P 63mc, respectively). Both variants of the phase transition to the ferroelectric phase are discussed based on the Landau theory. Electron paramagnetic resonance and magnetic susceptibility measurements reveal an onset of one-dimensional antiferromagnetic ordering below ≈ 220 K which develops fully near 140 K and, below TN ≈ 59 K, it transforms into a threedimensional antiferromagnetic order.