The propagation of cosmic ray (CR) protons in the Galaxy is discussed under the framework of a three-dimensional convection–diffusion model. Starting with the assumption of a uniform and continuous distribution of CR sources injecting CRs continuously in the Galaxy and by invoking a supernova explosion at various distances from the Earth, it is found that only those sources located within a distance of ∼1.5 kpc can produce appreciable temporal fluctuations in the CR proton flux observed near the Earth. So, the construction of the local CR proton spectrum is discussed by separating the contributions of the distant sources from that of the nearby sources. The contribution from the distant sources is treated in the framework of a continuous source distribution model in both space and time, but that of the nearby sources in a discrete space–time source model. The study predicts the presence of at least one old nearby source with a characteristic age of ∼105 yr located at a distance of ∼0.1 kpc to explain the observed proton flux below ∼100 GeV.