In 2020–2023, Lomonosov MSU has been developing postprocessing algorithms and software for airborne gravimeters based on navigation-grade strapdown inertial measurement units (IMUs). The focus was made on the potential of strapdown gravimeters to be used under dynamic flight conditions. This is of high demand in the present-day aerogeophysical surveys conducted using the so-called draped flights (that is, following the terrain). The developed postprocessing algorithms were implemented in the software suite of programs, which were widely tested using state-of-the-art strapdown airborne graivmeters. In the paper, gravimetry results from a new strapdown system (AGP-Grav) are presented. The cross-over analysis of the results shows that the new strapdown gravimeter can achieve a measurement precision of 1.4 mGal (root-mean-square error) under the draped flight conditions given a smooth drape flight surface. We also compare the gravity disturbances derived from AGP-Grav with gravity data obtained from another IMU (iMAR), which operated side-by-side with AGP-Grav in one of the flights. The results from both sensors are similar, with a root-mean-square error of the differences of 0.9 mGal. The paper also describes the developed postprocessing software programs, which cover all postprocessing stages from the quality control of raw IMU and GNSS data to calculation of the gravimetry solutions on the aircraft flight path.