Estimating the depth of a moving source with unknown source range is always a challenging problem in shallow water waveguides. The method of estimating the current motion source depth is sensitive to the unknown initial range and requires the horizontal synthetic aperture length formed by the motion of the source to be much longer than the modal interference period. Presented in this work is a method to estimate the depth of moving source based on the incoherently matched beam-wavenumber. In the beam-wavenumber domain, each peak amplitude only contains the modal excitation related to source depth, and each peak position corresponds to the mode propagation angle and the horizontal wavenumber. In this method, the received data are first used to perform beam-formed transformation in the vertical depth and horizontal synthetic aperture direction, and transformed into the beam-wavenumber domain. Then beam-wavenumber peak amplitudes are extracted and incoherently matched with the modal depth function to estimate the source depth. The proposed method is used to eliminate the unknown distance dependent term and improves the mode resolution by performing mode separation in the beam-wavenumber two-dimensional domain. The prominent feature of this method lies in realizing the source depth estimation at the unknown initial range and the horizontal synthetic aperture length which is smaller than the mode interference period. The simulation and SWellEx-96 experimental data processing results validate the superior performance of the proposed method.