A neutron monitor (NM) is a ground- (or sea-) based detector of the flux of cosmic ray particles in space. The high-energy cosmic rays in the GeV primary range interact in the upper atmosphere, producing a cascade of subatomic particles, some of which reach Earth’s surface. A neutron monitor is mostly sensitive to the neutron component of the atmospheric cascade. These neutrons can then be detected by induced nuclear fission of $^{10}$B in a $^{10}$BF$_3$ gas proportional counter. The Changvan neutron monitor is a portable neutron monitor assembled in Thailand and housed in a standard insulated shipping container to conduct long-term research in polar regions. There are three proportional counters housed in the insulated shipping container, but the central counter lacks the lead producer. We performed a Monte Carlo Simulation for the yield function of the Changvan monitor to primary particles. We validated our preliminary yield function by comparing count rates from simulation with actual data. We found that the maximum difference of the unleaded/leaded count rate ratio between simulation and experimental data was less than 7%. This leads to a promising yield function that can be used to determine the spectral index of relativistic solar ions with a single detector.