A novel approach for quantitative analysis in total-reflection X-ray fluorescence (TXRF) which can be employed for the samples with complex matrices inducing overlapping spectral signals in the scenario of limited availability of standard samples is proposed. The approach is based on the least squares (LS) decomposition of real spectra into the weighted sum of simulated individual element subspectra and requires only a single sample of matrix-matched reference material. Oceanic polymetallic nodules and crusts, having complex mineral matrix and containing high concentrations of overlapping elements, were chosen to demonstrate the feasibility of the approach in quantification of 11 elements. The comparison of the results obtained with LS decomposition, internal standard and linear calibration with three standard samples was performed. It was demonstrated that the performance of the proposed approach and of the linear calibration was better than that of internal standard for most of the elements; however, the proposed method requires only a single standard sample.