The unidentified source IGR J16328-4726 was covered with INTEGRAL observations for a long period (~9.8Ms) and was undetectable for most of the time while showing a very recurrent micro-activity with a duration from tens minutes to several hours. We report the discovery of two strong outbursts started at 53420.65 MJD and 54859.99 MJD respectively, the first with a duration of ~1 hour and the second with a lower limit on the duration of ~3.5 hours. Furthermore, the source have been detected in nine other short pointings with significance between 4 and 5 sigma as well as in a one of the revolution (during the exposure ~ 130 ks) at a significance level of ~7 sigma. The stronger outburst spectrum is well described by a power law model with a photon index of ~2.0 and a flux of ~3.3x10^{-10} erg cm^{-2} s^{-1} in the 20-50 keV energy band. The weaker outburst and revolution spectra show the same spectral shape and different fluxes. The combined timing and spectral properties observed during the outburst, the recurrent nature of this transient source, the Galactic Plane location, a dynamic range >170 in the 0.3-10 keV band and >165 in the 20-50 keV and the presence of a IR star in the error circle of an XRT/Swift pointing are suggesting this source as a member of the class of the Supergiant Fast X-ray Transients.