The invention relates to a drilling rig with a drilling tower, a base structure, on which the drilling tower is arranged, and at least three support units being part of the base structure, each support unit having at least one wheel rotatable around a horizontal wheel axis, wherein at least one of the support units comprises a vertical steering axis, around which the at least one wheel can be turned by a steering drive. The invention further relates to a method for moving such a mobile drilling rig.