Context.Based on the expansion velocities of their circumstellar shells, Galactic centre (GC) OH/IR stars can be divided into two groups that are kinematically different and therefore believed to have evolved from different stellar populations. Aims.We studied the metallicity distribution of the OH/IR stars population in the GC on the basis of a theoretical relation between EW(Na), EW(Ca), and EW(CO) and the metallicity. Methods.For 70 OH/IR stars in the GC, we obtained near-IR spectra. The equivalent line-widths of Na I, Ca I, 12CO(2, 0), and the curvature of the spectrum around 1.6 ?m due to water absorption were determined. Results.The near-IR spectrum of OH/IR stars is influenced by several physical processes. OH/IR stars are variable stars suffering high mass-loss rates. The dust that is formed around the stars strongly influences the near-IR spectra and reduces the equivalent line-widths of Na I and Ca I. A similar effect is caused by the water content in the outer atmosphere of the OH/IR star. Because of these effects, it is not possible to determine the metallicities of these stars with our low-resolution near-infrared spectroscopy.