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Localization is a key problem of mobile robot in the field for robot navigation and control, which directly affects the accuracy. A new relative localization method of pointpoint scan matching for the mobile robot was proposed based on laser range finder to achieve the matching of complex environment information under the continuous state by using the displacement theory of Fourier transform and Fourier-Mellin invariant of similarity transformation. This method is inspired by the image matching and curve matching domain, which is based on Fourier-Mellin transform method. Firstly, environmental information was obtained in different continuous time of the robot; the previous state was set as a reference scan and the latter state was set as the current scan. The mathematical model of relative positioning parameter was established. Then, the dimension was reduced. The 1D Fourier-Mellin was used three times continuously to get the rotational and translational increment. Thirdly, the comparative experiment was carried out with a featurefeature method based on the extracted corner features. Finally, the mobile robot path line was surveyed under an indoor environment and the laser data were collected for simulating track circuit diagram which were compared with the real conditions of track circuit. The experimental results further demonstrated the effectiveness, superiority and adaptability of the proposed method. It is no need to extract features from environment and it also has high antinoise and low computational lost. 