A novel transport algorithm performing proton track-structure calculations in arbitrary materials was developed. Unlike conventional algorithms, which are based on the dielectric function of the target material, our algorithm uses a total stopping power formula and single-differential cross sections of secondary electron production. The former was used to simulate energy dissipation of incident protons and the latter was used to consider secondary electron production. In this algorithm, the incident proton was transmitted freely in matter until the proton produced a secondary electron. The corresponding ionising energy loss was calculated as the sum of the ionisation energy and the kinetic energy of the secondary electron whereas the non-ionising energy loss was obtained by subtracting the ionising energy loss from the total stopping power. The most remarkable attribute of this model is its applicability to arbitrary materials, i.e. the model utilises the total stopping power and the single-differential cross sections for secondary electron production rather than the material-specific dielectric functions. Benchmarking of the stopping range, radial dose distribution, secondary electron energy spectra in liquid water, and lineal energy in tissue-equivalent gas, against the experimental data taken from literature agreed well. This indicated the accuracy of the present model even for materials other than liquid water. Regarding microscopic energy deposition, this model will be a robust tool for analysing the irradiation effects of cells, semiconductors and detectors.