We have addressed the problem of estimating surface-wave phase velocities through the spectral processing of seismic data. This is the key step of the well-known near-surface seismic exploration method, called multichannel analysis of surface waves. To increase the accuracy and ensure the unambiguity of the selection of dispersion curves, we have developed a new version of the frequency-wavenumber (f-k) transform based on the S-transform. We obtain the frequency-time representation of seismic data. We analyze the obtained S-transform frequency-time representation in a slant-stacking manner but use a spatial Fourier transform instead of amplitude stacking. Finally, we build the f-k image by analyzing the spatial spectra for different steering values of the surface-wave group velocities. The time localization of the surface-wave packet at each frequency increases the signal-to-noise ratio because of an exclusion of noise in other time steps (which does not fall in the effective width of the corresponding wavelet). The new f-k transform, i.e., the slant f-k (SFK) transform, renders a better spectral analysis than the conventional f-k transform and yields more accurate phase-velocity estimation, which is critical for the surface-wave analysis. The advantages of the SFK transform have been confirmed by synthetic- and field-data processing.