The effective potential in the Grumiller's modified gravity includes the Newtonian potential and a Rindler term. The fitting to the rotation curve data of eight galaxies suggests a universal Rindler acceleration a approximate to 0.30 x 10(-10) ms(-2). We do a two-parameter fit first, with the mass-to-light ratio ((sic)(*)) and the Rindler acceleration (a) as free parameters. It is found that the data of six out of the eight galaxies fit well with the prediction of theory in the range 0 r less than or similar to 40 kpc, although the theoretical curves show a tendency of arising beyond this range. The Rindler accelerations of the six well-fitted galaxies have the same magnitude, with an average value (a) over bar approximate to 0.30 x 10(-10) ms(-2). Inspired by this fact, we then carry out a one-parameter ((sic)(*)) fit to the six galaxies, with a fixed at (a) over bar, and find that the theory can still reproduce the observation. The value of Rindler acceleration we get here is a quarter of that of Milgrom's modified Newtonian dynamics. For the rest two galaxies, NGC 5055 and DDO 154, the fitting results are significantly improved if the photometric scale length (h) is included as another free parameter.