The achievement of the national gravity reference network of Republic of Moldova (NGRNM) represents the first step in merging gravity networks of Romania and Republic of Moldova. The project started as a joint venture of the Institute for Geophysics and Geology of the Academy of Sciences of Republic of Moldova and the Geological Institute of Romania. It is part of a larger program, GRANAT (Gravity Networks Advanced Ties), aimed to join gravity images over the state borders of Romania, Ukraine and Republic of Moldova, in an area where several major geotectonic units met each other along the SW margin of the East European Plate. The paper mainly deals with problems connected to gravity determinations along the NGRNM ties and their adjustment. The NGRNM consists of seven first order gravity stations regularly spaced over the Moldavian territory. They have been tied within a triangle network with central base station (Chisinau) by using a LaCoste & Romberg model D gravity meter. Gravity vertical gradient determinations in every base station have been also performed by repeated measurements at every site at two different levels: 0.30 meters, and 0.80 meters above the ground. The NGRNM has been adjusted by least square method as a free network, using four stochastic models based on various weighting systems. Provisional absolute gravity values within the NGRNM have been obtained by connecting the new network to the national reference networks of Romania.