Abstract:  Underwater sound propagation signal can be regarded as the composition of normal modes.Acoustic mode filtering is employed to separate each mode from the received signal and has been widely used in many practical applications，such as matched mode processing(MMP)for target localization，reconstruction of target signal，and so on.For a vertical line array，pseudo－inverse method is a popular and suitable way to implement mode filtering.A key problem for the pseudo－inverse method is to determine how many normal modes should be adopted to construct the coefficient matrix.Once the number of normal modes used by the pseudo－inverse method diverges from the actual value，performance of the mode filtering would decrease.In view of the above question，a method based on underdetermined blind source separation(UBSS)is proposed in this paper，aiming to search the number of normal modes contained in the received signal of a vertical line array.Therefore，traditional acoustic pseudo－inverse mode filtering can be decomposed in two steps.Firstly，one should search the number of normal modes by the present method.Then，one could filter each mode by the traditional way of pseudo－inverse mode filtering.To verify the present method，acoustic pressure field in two kinds of waveguide，ideal waveguide and shallow water waveguide in summer，has been simulated numerically.Results of the numerical simulation show that：(1)one can extract the number of the normal modes contained in the received signal of vertical line array by the proposed method when the signal to noise ratio(SNR)is high；(2)the performance of the method will decrease as the SNR reduces.It is assumed that the present method can be used to diminish the deviation of mode filtering caused by the uncertainty of the number of normal modes.And the method has potential use in practical applications based on mode filtering，for instance，target localization and identification.