The neutron dose resulting from external irradiation can be evaluated by measuring the counts of characteristic γ rays produced by 24Na in the human body. The detecting geometry with the highest detection efficiency for measuring the whole body 24Na activity has not been studied. In this work, the MCNP code is used to calculate the spatial distribution of 24Na in the human body irradiated by neutrons with different energies in different irradiation geometries. The fluence distribution of 24Na characteristic γ rays at the body surface is calculated. The counts of 24Na characteristic γ rays induced by monochromatic neutrons irradiation are simulated to fit the scenarios of neutron irradiation by a continuous energy spectrum neutrons. When the spontaneous neutrons from 252Cf with 1 Gy dose irradiate the human body, (3.63 - 4.35) × 1010 24Na atoms are produced. The lower detection limit for the neutron absorbed dose is reduced from ~100 mGy to less than 1 mGy when the radiation detector is placed over the back of the human body close to the liver. The relative error between the measured counts of 24Na characteristic γ rays caused by 252Cf neutrons irradiation and the counts fitted by monochromatic neutron irradiation data is less than 5.7%. The neutron dose received from a continuous energy spectrum neutron can be acquired quickly and accurately by weighted summing the data for monochromatic neutron irradiations calculated in this paper, which is more convenient and practical than the previous method.