High-resolution gravity anomalies on the surface of the Moon are determined from Lunar Prospector tracking data residuals. By means of a benchmark test the recovery method is validated with respect to the orbit determination and gravity field recovery strategy. Tracking data for the entire extended mission of Lunar Prospector, during which the satellite flew at an average altitude of 30 km above the lunar surface, have been completely and independently processed and orbits have been determined. Using tracking data residuals from these precise orbits, adjustments to the a priori gravity field model have been created for Mare Serenitatis. The results for Mare Serenitatis with the local recovery are comparable to global recovery results, yet faster and more efficient with a possibility to increase the resolution.