A non-linear differential equation is analyzed to determine the geodesic curves on ruled surfaces with time-like rulings in My. When it is assumed that curvature and torsion of the base curve and components with respect to Frenet's frame of time-like straight-line are constants, for a special integration constant, it appears that the resulting non-linear differential equation can be integrated exactly. Finally, examples are given to show the geodesic curve on ruled surfaces with time-like rulings.