We present new photometric and spectroscopic observations of an unusual luminous blue variable (LBV) in NGC 3432, covering three major outbursts in 2008 October, 2009 April and 2009 November. Previously, this star experienced an outburst also in 2000 (known as SN 2000ch). During outbursts the star reached an absolute magnitude between -12.1 and -12.8. Its spectrum showed H, He I and Fe II lines with P-Cygni profiles during and soon after the eruptive phases, while only intermediate-width lines in pure emission (including He II lambda 4686) were visible during quiescence. The fast-evolving light curve soon after the outbursts, the quasi-modulated light curve, the peak magnitude and the overall spectral properties are consistent with multiple episodes of variability of an extremely active LBV. However, the widths of the spectral lines indicate unusually high wind velocities (1500-2800 km s-1), similar to those observed in Wolf-Rayet stars. Although modulated light curves are typical of LBVs during the S-Dor variability phase, the luminous maxima and the high frequency of outbursts are unexpected in S-Dor variables. Such extreme variability may be associated with repeated ejection episodes during a giant eruption of an LBV. Alternatively, it may be indicative of a high level of instability shortly preceding the core-collapse or due to interaction with a massive, binary companion. In this context, the variable in NGC 3432 shares some similarities with the famous stellar system HD 5980 in the Small Magellanic Cloud, which includes an erupting LBV and an early Wolf-Rayet star.