The Equation of State (EOS) of pure neutron matter at zero temperature is calculated up to five saturation densities within the Brueckner theory with the inclusion of three-body forces. Three different realistic and accurate two-body forces are considered to evaluate the G-matrix effective interaction for nuclear matter. These models are the chiral N3LO, the CD-Bonn and the Argonne V18, which give quite different EOS. Two types of three-body forces are included to the effective interaction, which might be important at densities several times that of nuclear matter density. Using a microscopic EOS for pure neutron matter, static properties of non-rotating neutron stars such as masses and radii are evaluated. The resulting maximum masses of neutron star using different interactions near 2 Mʘ are found to be in reasonable agreement with the measured ones PSR J1614−2230 (with Mmax = 1.97 ± 0.04 Mʘ) and PSR J0348+0432 (with Mmax = 2.01 ± 0.04 Mʘ).