Neutron beam can be produced in different nuclear reactions. One can not accelerate neutrons like charged particles, but beginning with high energy neutron, we can obtain a vast range of lower energy by colliding them to the environment atoms like, graphite and water. The resulted neutrons can have very low energy, so one can produce a source of thermal neutrons(less than 1 eV). There in Indian Atomic Centre BHABHA by putting 6 neutron sources (Am/Be) in a graphite moderator, they produced a thermal source and used it for calibrating the thermal neutron detectors. Neutron flux distribution, in the above mentioned Centre, have been measured by a neutron activation procedure. In the first part of this thesis, we calculated the neutron flux distribution in the above mentioned structure by MCNPX code and the output results were compared with experimental data from BHABHA Atomic Centre. Measured results were in good agreement with the experimental data from BHABHA centre, which shows that our simulation program is accurate enough to set up a similar calibration for the neutron detectors. Then using the code and neutron source moderated by water (at MALEK ASHTAR UNIVERSITY) we calculated counting calibration coefficient of BF 3 detector. For this purpose, we firs simulated a neutron source in water environment and then, in a certain distance from the source, the neutron flux was calculated. Using the calculated flux, we determined the counting of the detector. In the second part, by putting a detector in the place we measured counting rate experimentally and at last using the measured and the calculated values, we determined the counting calibration coefficient. Key words: MCNPX, Neutron Source, BF 3 detector, Calibration Coefficient, Graphite Moderator.