The paper presents the core design, model development and results of the neutron transport simulations of the large Pressurized Water Reactor based on the AP1000 design. The SERPENT2.1.29 Monte Carlo reactor physics computer code with ENDF/BVII and JEFF 3.1.1 nuclear data libraries was applied. The full-core 3D models were developed according to the available Design Control Documentation and the literature. Criticality simulations were performed for the core at the Beginning of Life state for Cold Shutdown, Hot Zero Power and Full Power conditions. Selected core parameters were investigated and compared with the design data: effective multiplication factors, boron concentrations, control rod worth, reactivity coefficients and radial power distributions. Acceptable agreement between design data and simulations was obtained, confirming the validity of the model and applied methodology.