In this paper we address the camera parameter estimation problem using an arbitrary planar calibration object. We intend not to use a system of linear or nonlinear equations in terms of the camera parameters derived from the correspondence relationships between the image features (points or lines) and the object features. Instead, we assume that the shape of the planar object can be arbitrary. Therefore, there may not exist any extractable object point or line features. We formulate the estimation method as a generate-and-test method. To make the method effective, we reduce the dimensionality of the parameter space from six to two using a simplified model of the perspective transformation under some mild conditions. Furthermore, several other measures are also taken to cut down the generation time and the verification time. Real, computer-generated, and noisy imagery data are used to illustrate our method in the experiments. The statistics on the speed performance of the method are also included.