We present a method of directly estimating surface mass anomalies at regional scales using satellite-to-satellite K-band Ranging (KBR) data from the Gravity Recovery and Climate Experiment (GRACE) twin-satellite mission. Geopotential differences based primarily on KBR measurement are derived using a modified energy integral method with an improved method to calibrate accelerometer measurements. Surface mass anomalies are computed based on a downward continuation process, with optimal regularization parameters estimated using the L-curve criterion method. We derive the covariance functions in both space-and space-time domains and use them as light constraints in the regional gravity estimation process in the Amazon basin study region. The space-time covariance function has a time-correlation distance of 1.27months, which is evident that observations between neighboring months are correlated and the correlation should be taken into account. However, most of the current GRACE solutions did not consider such temporal correlations. In our study, the artifact in the regional gravity solution is mitigated by using the covariance functions. The averaged commission errors are estimated to be only 6.86% and 5.85% for the solutions based on the space-covariance function (SCF) and the space-time covariance function (STCF), respectively. Our regional gravity solution in the Amazon basin study region, which requires no further post-processing, shows enhanced regional gravity signatures, reduced gravity artifacts, and the gravity solution agrees with NASA/GSFC's GRACE MASCON solution to about 1cm RMS in terms of water thickness change over the Amazon basin study region. The regional gravity solution also retains the maximum signal energy while suppressing the short wavelength errors.