The local tie vector, which connects the different space geodetic techniques at a co-located site, plays an important role in the realization of the International Terrestrial Reference Frame (ITRF). This paper presents a new method to determine the tie vector between the GNSS and very long baseline interferometry tracking points. The parameters of the local tie vector and the axes offsets are introduced into constraint equations. The parameters are then resolved using the 3D constrained least squares adjustment. With the surveying data collected at two different sites (Kunming and Urumqi) in China, the proposed method can precisely determine the local tie vectors in a geocentric frame. The root mean square error (RMSE) is (1.2, 2.3 and 1.5 mm) and (1.0, 1.5 and 1.4 mm) for the three coordinate components at the sites in Kunming and Urumqi, respectively. The offset between the primary and secondary axes of the VLBI telescopes is estimated to be 7.5 mm in Kunming's site and 4.0 mm in Urumqi's site, and the corresponding RMSE is 1.8 mm and 2.0 mm for the two sites, respectively.