A shift three-source model is used in this paper to describe the multiplicity and the pseudorapidity distributions of final-state charged particles produced in proton-proton collisions at energies available at the Large Hadron Collider (LHC). The three kinds of sources are central sources arising from gluon-gluon collisions, target fragmentation sources arising from gluon- or quark-induced collisions with target quarks, and projectile fragmentation sources arising from gluon- or quark-induced collisions with projectile quarks. The central, target fragmentation, and projectile fragmentation sources each have shifts around their centers. The results calculated by using the shift three-source model are in agreement with the experimental data of the ALICE (A Large Ion Collider Experiment) and the CMS (Compact Muon Solenoid experiment) Collaborations.