The work aims to realize the in-situ fast calculation of the removal function for ion beam polishing by Faraday cup scanning based on BP neural network. For ion beams with different spatial distributions, the information of the current density distribution was determined by Faraday cup scanning, and the information of the removal function was determined by etching experiment. A BP neural network was used to fit the relationship between current density distribution and removal function distribution. The BP neural network created was a three-layer back propagation neural network, containing one hidden layer. The input signal of the BP neural network was the full width at half height of the ion beam current density and the output signal was the full width at half height of the removal function. After 408 iterations, the mean square error of the BP neural network was 2.451×10?10. Based on this, the model to calculate the distribution information of the removal function based on BP neural network was established. With this model, the in-situ fast calculation of the removal function could be realized and used for ion beam polishing. For a set of ion source determined parameters, the peak current density obtained by Faraday cup scanning was 0.722 mA/cm2 with a full width at half height of 13.923 mm. The removal function obtained by the groove etch experiment had a peak removal rate of 1.153 nm/s, a full width at half height of 12.899 mm, and a volumetric removal rate of 0.012 898 mm3/s. According to the current density distribution, the removal function calculated by the established BP neural network model had a peak removal rate of 1.192 nm/s, with a full width at half height of 13.006 mm and a volumetric removal rate of 0.013 556 mm3/s, respectively. The error between the volume removal rate of the removal function calculated by the BP neural network and the experimental method was 5.09%, which met the requirements of optical ultra-precision polishing. Ion beam polishing experiment was carried out by the calculated removal function on a 320 mm diameter fused silica element. After ion beam polishing, the PV value of the surface of the optical element decreased to 0.197λ (wavelength λ=632.8 nm), and the RMS value decreased to 0.009λ, which realized the ultra-precision polishing of optical element surfaces. The convergence rate in the polishing process reached 4.19. The experimental results showed that the BP neural network established could bring about the in-situ fast calculation of the removal function for ion beam polishing. The accuracy of the removal function calculated from this model met the demand for ultra-precision processing of optical components. The model is applicable to the calculation of removal functions for fused silica and other material optics. The time to determine the removal function using this model is reduced from 2 hours to 2 minutes, which improves the efficiency of ion beam polishing.