Results are reported of an investigation on the velocity of a single straight magnetic domain wall in a Ga:YIG film as a function of the drive field and of a static magnetic field applied perpendicular to the wall in the plane of the film. At all drive fields a substantial increase of the wall velocity was observed when the in-plane field was applied. At an in-plane field of about 400 Oe and at a rather low drive field (2.4 Oe above the coercive field) a maximum value in wall velocity of 270 ms-1was observed. At higher drive fields the wall velocity decreased to a constant value of 110 ms-1, independent of the drive field. This behavior can be explained by extending Slonczewski's theory of domain wall motion to the present case. From the observed wall mobility parameter we have calculated the reduced Landau-Lifshitz damping constant ( Oe2s). This value is near to the value obtained by Spencer and LeCraw from linewidth measurements in FMR on Ga:YIG spheres ( Oe2s).