The neutron beam facility at NCSR “Demokritos” is driven by a 5.5 MV tandem T11/25 Van De Graff accelerator that provides continuous, high intensity ion beams. Depending on the neutron production reaction, different energy regions of neutron beams are available. Neutron fields with well defined energies are produced by means of nuclear reactions such as: 7Li(p,n)7Be, 3H(p,n)3He, 2H(d,n)3He and 3H(d,n)4He, delivering neutrons up to the energy of ~28 MeV. In order to fully characterize the neutron beam at NCSR “Demokritos”, in the framework of the present work, the CONY C++ computer code has been developed. The implementation of the code for the 7Li(p,n)7Be and 3H(d,n)4He reactions is discussed. The method of calculation of differential neutron yields by thin and thick targets is described. Specifically, for the reaction 7Li(p,n)7Be the mathematical singularity at near threshold energies is discussed along with the method that was used as to overcome this issue. Finally, the results of the code including the double differential neutron yields, the neutron beam energy distribution at the sample position and the total neutron yields have been compared with experimental data as well as with the results of the NeuSDesc software (JRC-IRMM: Neutron Source Description).