Diffusion-ordered NMR spectroscopy (DOSY) presents an essential tool for the analysis of compound mixtures by revealing intrinsic diffusion behaviors of mixed components. The applicability of DOSY measurements on complex mixtures is generally limited by the performance of data reconstruction algorithms. Here, based on constraints on low rank and sparsity of DOSY data, we propose a reconstruction method to achieve high-resolution DOSY spectra with excellent peak alignments and accurate diffusion coefficients for measurements of complex mixtures even when component signals are congested and mixed together along the spectral dimension. This proposed method is robust and suitable for DOSY data acquired from common commercial NMR instruments; thus, it may broaden the scope of DOSY applications.