The integrated navigation gravity measurement system, composed of laser gyroscope-based inertial navigation systems, has gradually expanded its application in the fields of aviation, navigation, and vehicle gravity measurement. The disturbance of carrier acceleration needs to be suppressed to improve the accuracy of gravity measurement. Therefore, filtering the gravity data is of crucial importance. Traditional gravity data filtering methods are constrained by fixed long time delays, which directly leads to the functional limitation of application scenarios such as gravity matching. To address these challenges, a real-time gravity data processing method based on neural network fitting filtering was proposed in this investigation. By approximating the Finite Impulse Response (FIR) filter through neural network implementation, the long dependency on future data was effectively reduced, resulting in minimized time delays. Experimental verification demonstrated that the delay of the designed method was reduced by 93% compared with the FIR filter, significantly improving the real-time performance of data processing while maintaining a high accuracy, providing a solution for the real-time gravity measurement of the laser gyroscope inertial group gravity measurement system.