Active neutron multiplicity counting method could provide the multiplicity distribution of neutrons multiplied from one fission event induced by an external neutron source in nuclear components. The equivalent mass of material in uranium component can be obtained by substituting the neutron multiplicity counting into the mass inversion equation with the known characteristic parameters. Therefore, this method is widely used in nuclear material accounting, nuclear security measurement and arms control verification. In this paper, Mont Carlo neutron transport calculation was used to simulate the experiment of the uranium mass estimation by classical point model equation. Based on this, an improved equation is proposed, which could significantly reduce the effect of source-sample coupling and neutron back irradiation on the accuracy of uranium mass estimation for the experiment. The validity of the mass equation is tested by numerical method, and the deviation between real mass and estimated mass obtained by the original point model equation and the improved mass equation is compared. The active neutron multiplicity counting simulation calculation is realized based on the original neutron transport simulation software. A model of active neutron multiplicity counting detection system and 32 models of uranium metal hemispherical shell are established. The active neutron multiplicity counts of DT source and AmLi source with different distances from uranium components are simulated and the estimated mass of the object are obtained with the simulated results. The numerical simulation results show that the average deviation of the improved uranium component mass inversion is reduced to less than 10%.