Geometric scaling is well confirmed for transverse momentum distributions observed in protonproton collisions at LHC energies. We introduced multiplicity dependence on a saturation momentum of the geometrical scaling, assuming the scaling holds for semi-inclusive distributions as well as for inclusive distributions. The saturation momentum is usually given by Bjorken's x variable, but redefinition of the scaling variable can make the saturation momentum a function of collision energy W . We treat the energy as a free parameter (denoted W * to distinguish it from W ) and associate the energy-dependent saturation momentum Qsat(W * ) with particle number density. By using Qsat(W * ) for a scaling variable τ , we show semi-inclusive distributions can be geometrically scaled. i.e., all semi-inclusive spectra observed at W =0.90, 2.76 and 7.00 TeV overlap one universal function. The particle density dependences of mean transverse momentum pT for LHC energies scales in terms of Qsat(W * ). Furthermore, our model explains a scaling property of event-by-event pT fluctuation measure √ Cm/ pT at LHC energies for pp collisions, where Cm is two-particle transverse momentum correlator. Our analysis of the pT fluctuation makes possible to evaluate a non-perturbative coefficient of the gluon correlation function.