A number of techniques are available for acoustic source localization in isotropic plates without knowing the material properties of the plate. However, for a highly anisotropic plate acoustic source localization requires some knowledge of the plate material properties or its group velocity profile. In absence of this information one requires a large number of sensors to predict the acoustic source point in the plate. All proposed techniques for acoustic source localization with a few sensors assume the straight line propagation of waves from the source to the receiving sensor with an average group velocity when the plate material properties are not known. However, this assumption is not true for an anisotropic plate. Although the currently available techniques work well for weakly anisotropic plates since the wave path does not deviate significantly from the straight line propagation they fail miserably for highly anisotropic plates. In this paper acoustic source is localized in an anisotropic plate when non-circular wave front is generated. Direction vectors of wave fronts are obtained from the Time-Difference-Of-Arrivals (TDOA) at three sensors placed in a cluster. Four such direction vectors are then utilized in geometric vector analysis to accurately obtain the acoustic source location. The proposed technique is illustrated on an orthotropic plate that generates rhombus shaped wave front. It should be noted that the proposed technique does not require wave propagation along a straight line from the source to the sensor. It also does not need the knowledge of the material properties of the plate.