A curve is named as rectifying curve if its position vector always lies in its rectifying plane. There are lots of papers about rectifying curves in Euclidean and Minkowski spaces. In this paper, we give some relations between extended rectifying curves and their modified Darboux vector fields in Galilean 3Space. The other aim of the paper is to introduce the ruled surfaces whose base curve is rectifying curve. Further, we prove that the parameter curve of the surface is a geodesic.