The objective of this study was to propose a novel preprocessing approach to simultaneously correct for the frequency and phase drifts in MRS data using cross-correlation technique. The performance of the proposed method was first investigated at different SNR levels using simulation. Random frequency and phase offsets were added to a previously acquired STEAM human data at 7 T, simulating two different noise levels with and without baseline artifacts. Alongside the proposed spectral cross-correlation (SC) method, three other simultaneous alignment approaches were evaluated. Validation was performed on human brain data at 3 T and mouse brain data at 16.4 T. The results showed that the SC technique effectively corrects for both small and large frequency and phase drifts, even at low SNR levels. Furthermore, the mean square measurement error of the SC algorithm was comparable to the other three methods used, with much faster processing time. The efficacy of the proposed technique was successfully demonstrated in both human brain MRS data and in a noisy MRS dataset acquired from a small volume-of-interest in the mouse brain. The study demonstrated the availability of a fast and robust technique that accurately corrects for both small and large frequency and phase shifts in MRS.