To overcome the inherent fixed time-delay limitation of conventional gravity filtering methods in laser gyro-based inertial navigation gravity measurement systems, this paper proposes a real-time gravity data processing method based on neural network-approximated FIR (finite impulse response) filtering. By fitting the FIR filter through neural network implementation, the long dependency on future data was effectively reduced, thereby effectively reducing filtering delay. Experimental results show that compared with the FIR filter, the processing delay of the proposed method is reduced by 93%, and the average filtering accuracy is better than 2mGal. This indicates that the proposed method can significantly improve the real-time performance of data processing while maintaining high accuracy, providing a solution for the real-time gravity measurement of the laser gyroscope inertial group gravity measurement system.