Using the VLA and the VLBA we have observed water maser emission in the proto-planetary nebula candidate IRAS 19134+2131, in which the water maser spectrum has double radial-velocity peaks separated by ˜100 km s-1. The main purpose of this study is to reveal the 3-D kinematics of the masers in detail, which indicates a fast ( ˜110 km s-1) bipolar flow seen only during ≤100 years at the proto-planetary forming stage. At the same time, we have measured the Galactic rotation of IRAS 19134+2131 and its distance on the basis of differential VLBI technique to precisely measure relative positions of the maser features with respect to the nearby extragalactic reference source J1925+2106. We obtain a secular motion of IRAS 19134+2131 of μ l=: -4.6±0.7 mas yr-1 along the Galactic plane toward the Galactic center. This indicates a ``far distance" (≥16 kpc) for IRAS 19134+2131, located in the fourth quadrant in the Galaxy, if the Galactic rotation curve remains flat at 220 km s-1.