The phase-matched filters are defined as a group of linear filters in which the Fourier phase of the filter is made equal to that of a given signal. In this article, the fundamental theory of phase-matched filters is described in detail, and on the basis of the given path dispersion curve the design of phase-matched filter is finished in theory. Finally, an effective method working on weak surface wave signals is developed. To test the validity of the method, it is applied to a set of nuclear explosions occurred on the Nevada Test Site and the magnitudes of these events are estimated. From comparing the Ms obtained from the method with ones reported by ISC（International Seismological Centre）, it is proved that the relative error is small, the design is effective to detect surface wave signal, and the signal-to-noise rate of weak surface wave signals can be enhanced .