Abstract: The early growth of neutron population within a supercritical system of fissile material is of a statistical nature and may depart significantly from the average time dependence neutron population. The probability of a source neutron sponsoring a persistent fission chain was considered for a supercritical system. Then the probability distribution in time of the neutron population reaching a preset level was deduced based on the probability P(n,t) of n neutron at time t. By combing the above two probabilities, the probability that at time t after the system reached critical there were n₀ neutron in the system was derived. The P(t) of Godiva neutron excursion at supercritical, and the pre-burst probability of BARS were calculated by this model, and were found agree with the experiment result.