Small earthquakes occur due to natural tectonic motions and are induced by oil/gas production processes. In many oil/gas fields and hydrofrackings there are induced earthquakes due to fluid extraction or injection. The location and source mechanisms of these earthquakes provide valuable information about the reservoirs. The analysis of induced seismic events always assumed a double-couple (DC) source mechanism. However, recent studies have shown a non-negligible percentage of a non-double-couple (non-DC) component of source moment tensor in hydraulic fracturing events assuming a full moment tensor source mechanism (Rutledge et al. 2003, Šílený et al., 2009; Warpinski and Du, 2010; Song and Toksöz, 2011). The rare uncertainty quantification of the moment tensor solution makes it hard to determine the reliability of these source models. In our study, we developed a waveform-based Bayesian full moment tensor inversion method to do the source relocation, full moment tensor inversion and uncertainty quantification for the induced seismic events. We conducted synthetic tests to validate the method before the application to the real data. Then we apply this new developed Bayesian inversion approach to real induced seismicity data in an oil/gas field in Oman.