We performed Pulse Shape Analysis to separate single-scattered gamma energy deposition events from multiple-scattered photons in a high-sensitivity γ -ray spectrometer. The spectrometer is based on a Broad Energy High Purity Germanium detector and the developed technique uses multivariate analysis by an application of the Multi-Layer Perceptron Neural Network. A very good separation of the single-site-and multi-site events was achieved leading to a significant reduction of the background level of the investigated spectrometer -the double escape peak, rich in singlesite events, was reduced by 95%, while the full energy peaks lost at most 25% of their counts. The peak to Compton ratio, calculated for the 2614.5 keV gamma line from 208 Tl, was improved by 114.3%.