The track multiplicity distribution of emitted charged particles in the collisions of hadrons is one of the observables for understanding multiparticle production in proton-proton collisions at high energy. It imposes some important constraints in the particle production mechanisms. It has been the subject of experimental and theoretical studies and provides essential information on the dynamics of strong interactions. This work covers the measurements of maximum track densities on the data recorded in proton-proton collisions at the center of mass energy √ s =13 TeV using the Compact Muon Solenoid (CMS) detector at the Large Hadron Collider (LHC) at European Organization for Nuclear Research (CERN). The proton-proton data set from RunII (2015C) with 8.93 × 107 events were analyzed. The measurements were performed using high multiplicity events which were collected in the High Multiplicity Trigger. The main goal is to make comparisons between the results obtained previously at a low center of mass-energy and higher energy for the maximum track density per event inside a small window with width 0.1, 0.2, and 0.5 with respect to pseudorapidity to check if there is any irregularity. In order to reject secondaries and background processes a selection was applied to the data. The maximum track density, < dndη >max, distributions within several pseudorapidity windows (∆η = 0.1, 0.2 and 0.5) were analyzed. It was found to be larger in a smaller window ∆η = 0.1 when compared with the larger windows. The results show that the maximum charged particle density per given pseudorapidity interval increases linearly with track multiplicity.