Aiming at the passive impulse wideband source range problem in shallow water waveguides, a passive source range method with single hydrophone based on the matched mode processing is presented in this paper, the method is applied to the shallow water waveguide with a bottom of liquid semi-infinite space. Warping transformation is a useful tool to separate the normal modes of the received signals of the impulse source, and the frequency domain signals of each order can be obtained. The seafloor phase shift parameter is an important parameter describing the acoustic parameters of the seafloor, which contains nearly all the information about sea floor, what is more, the seafloor phase shift parameter is also an parameter that can be obtained by some experimental data easily. Each order normal mode can be represented by the expression that contains the phase shift parameter of sea floor. What is more, the influence of sound speed profile of the waveguide on eigenvalue can be approximately eliminated by jointly processing arbitrary two-order normal modes. Sound speed profile has a similar influence on eigenvalue of each order normal mode, therefore, the difference in the eigenvalues between arbitrary two-order normal modes can be approximated represented by the phase shift parameter of the sea-floor, the sea depth and the mean speed in the waveguide. In this way, the phase replica which consists of the eigenvalue difference of each two-order mode can be calculated simply and quickly, and then by constructing cost function and matching normal mode, the underwater impulse source can be located. Compared with the traditional method of processing matched mode and the method of processing matched fields, the method presented in this paper has two advantages: using warping transformation instead of hydrophone arrays to separate the normal modes; the replica can be calculated quickly and easily, depending on a small number of environmental parameters of waveguide. The effectiveness and accuracy of the method are proved by the results of numerical simulation and sea experimental data processing, in which the signals are both received by a single hydrophone. The sea experimental data contain linear frequency modulation impulse source signal and explosion sound source signal, and the mean relative error of range estimation is less than 10%. In the end of this paper, the range estimation error is analyzed, indicating that the error originates mainly from the mode phase parts besides the phase part of Hankel function. Consequently, finding the ways to reduce the range estimation error is an important project in the future.