Monte Carlo method has been used to determine the efficiency for proton production and to study the energy and angular distributions of the generated protons. The ENDF library of cross sections is used to simulate the interactions between the neutrons and the atoms in a polyethylene (PE) layer, while the ranges of protons with different energies in PE are determined using the Stopping and Range of Ions in Matter (SRIM) computer code. The efficiency of proton production increases with the PE layer thickness. However the proton escaping from a certain polyethylene volume is highly dependent on the neutron energy and target thickness, except for a very thin PE layer. The energy and angular distributions of protons are also estimated in the present paper, showing that, for the range of energy and thickness considered, the proton flux escaping is dependent on the PE layer thickness, with the presence of an optimal thickness for a fixed primary neutron energy.