Elastic scattering differential cross sections for a p-He-4 system are calculated within the framework of optical limit approximation of the Glauber multiple scattering model. Three different ranges for proton energy (E-lab), 19 < E-lab < 50 MeV, 100 <= E-lab <= 1730 MeV, and 45 <= E-lab <= 393 GeV are considered. It is shown that the Pauli blocking fails to describe the data up to the proton energy, E-lab < 100 MeV. For higher proton energies, a qualitative agreement is obtained. The observed elastic scattering differential cross section is nicely reproduced in the whole range of scattering angles in the center of mass system up to Theta(c.m.) < 200 degrees for 19 < E-lab <= 100 MeV when the effect of both the nucleon-nucleon (NN) phase variation parameter gamma(NN) and higher-order momentum transfer components (lambda(n), n = 1 and 2) of (NN) elastic scattering amplitude is included. In the range of 200 <= E-lab <= 1730 MeV, introducing lambda(n) plays a significant role in describing the data up to the momentum transfer, q(2) <= 1.2 (GeV/c)(2). Moreover, it is found that considering only the effect of phase variation parameter, gamma(NN), improved the agreement in the region of minima for elastic scattering differential cross section for 45 <= E-lab <= 393 GeV. The values of gamma(NN) and lambda(n) as a function of incident proton energies are presented.