A common problem in vanishing-point-based camera calibration methods is that they are ill-conditioned when the parallel lines for calibration in the world coordinates also appear to be parallel or near-parallel in the image coordinates. Then the camera parameters are not calculable or incur substantial error because one of the vanishing points approaches infinity. We propose a new method that overcomes the ill-conditioning. Using lane markings on a road to form a rectangular calibration pattern with two vanishing points, we first derive a set of equations based on one vanishing point without assuming any extrinsic parameters being known a priori. Because only one vanishing point can approach infinity at any one time, ill-conditioning can be avoided completely by selecting the vanishing point that does not suffer from it. This enables us to produce a set of extrinsic camera parameters that maps the world and image coordinates accurately. Simulation and real image tests show that the proposed method conquers ill-conditioning successfully and is insensitive to pixel offset on the calibration pattern.