The Glauber multiple-scattering theory is applied to the study of quasi-free scattering of high-energy protons by nuclei. The multiple scattering of the knocked-out nucleon is not considered. The differential cross-section is written as a sum of different terms corresponding to single, double, …, incoherent scattering of the incident nucleon inside the target nucleus. It is shown that the single-scattering term is similar to the outcome of the distorted-wave impulse approximation. The theory is compared with the experimental cross-section of the quasi-free scattering of 1 GeV protons from12C and the agreement is satisfactory at forward angles. The contribution from double-scattering terms appears to be rather important.