We have proposed a novel structure-oriented singular value decomposition (SOSVD) for enhancing useful reflections by removing random noise of seismic data. The SOSVD locally flattens the useful reflections by predicting each trace from its neighbouring traces. The plane-wave destruction (PWD) operator serves as the slope estimator for the prediction operator. In the flattened local processing window, we can apply a traditional SVD to remove incoherent noise. The SVD denoised windows are then stacked to output the denoised trace. Compared with GSVD, the SOSVD can preserve much more dipping events by slope flattening. Compared with LSVD, the SOSVD skips the use of dip steering that depends on a uniform shift for each trace and assumes a uniform-slope processing window, thus is more robust and effective in handling complex structures. Compared with $f-x$ deconvolution, the SOSVD can be significantly more effective both in the removal of random noise and the preservation of useful reflections.