Accurate beam range prediction during clinical treatment planning is key to improve targeted dose delivery in proton and heavy ion therapy. A substantial source of beam range uncertainty is the prediction of ion stopping power ratio (SPR) relative to water from an empirical calibration based on conventional x-ray computed tomography (CT) used in clinical practice today. The aim of this study was to investigate the potential of a novel spectral CT imaging technique based on a dual-layer detector-based approach to improve the SPR prediction for particle therapy treatment planning, an improvement that would minimize the beam range uncertainty and allow for reduced safety margins in the patient. Using calibrated and validated maps of electron density and effective atomic number from spectral CT data, predicted SPR values in tissue substitutes were within a mean accuracy of 0.6% compared to measured SPR and showed substantially better agreement with measured data compared to standard CT-number-to-SPR calibration. The accuracy of SPR was not affected by CT acquisition settings, reconstruction parameters, phantom size, and type. Additionally, various spectral CT conversion algorithms were compared to determine the most accurate prediction method. Dosimetric validation of the developed method using a half-head anthropomorphic phantom in a routine-like setting indicated that SPR prediction with dual-layer spectral CT outperforms the clinical single-energy CT standard with a range prediction improvement of 1 mm. This study demonstrated in homogeneous and heterogeneous phantoms that spectral CT is feasible for particle therapy planning to improve range estimates for high-precision particle therapy.