Abstract
In this paper, we study the position vector of an arbitrary curve in Galilean 3-space G3. We first determine the position vector of an arbitrary curve with respect to the Frenet frame. Also, we deduce in terms of the curvature and torsion, the natural representation of the position vector of an arbitrary curve. Moreover, we define a plane curve, helix, general helix, Salkowski curves and anti-Salkowski curves in Galilean space G3. Finally, the position vectors of some special curves are obtained and sketching.