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A noise-reduction method with sliding windows in the frequency-space (f-x) domain, called the local f-x Cadzow noise-reduction method, is presented in this paper. This method is based on the assumption that the signal in each window is linearly predictable in the spatial direction while the random noise is not. For each Toeplitz matrix constructed by constant frequency slice, a singular value decomposition (SVD) is applied to separate signal from noise. To avoid edge artifacts caused by zero percent overlap between windows and to remove more noise, an appropriate overlap is adopted. Besides fl at and dipping events, this method can enhance curved and conflicting events. However, it is not suitable for seismic data that contains big spikes or null traces. It is also compared with the SVD, f-x deconvolution, and Cadzow method without windows. The comparison results show that the local Cadzow method performs well in removing random noise and preserving signal. In addition, a real data example proves that it is a potential noise-reduction technique for seismic data obtained in areas of complex formations.