Passive localization of weak sources in the presence of strong interferences is generally a difficult task. In this paper, an eigenanalysis-based adaptive interference suppression (EAAIS) method is proposed for estimating the bearing and subsequently the weak source range. Assuming the target of interest (TOI) is in a known bearing sector, first we define a contribution ratio for each eigenvector of the cross-spectral density matrix (CSDM). The eigenvectors not dominated by the TOI are adaptively identified and removed for interference suppression. The remaining eigenvectors are then used to reconstruct the CSDM for TOI bearing estimation. Finally, the acoustic source range estimation is achieved with the reconstructed CSDM, by matching the beam intensity striation pattern, where it is not required to estimate the waveguide-invariant parameter. The effectiveness of the proposed TOI localization is demonstrated using several experimental data sets.