In this research, we introduce a reasonable noise model for range data which is obtained by a laser radar range finder, and derive two simple approximate solutions of the optimal local plane fitting the range data under the noise model. Then we compare our methods with the general least-squares based methods, such as Z-function fitting, the eigenvalue method, and the maximum likelihood estimation method, as well as the renormalization method, which is an iterative method to obtain the optimal fitting of planes of range data under the noise model. All the methods are compared and evaluated using both synthetic range data and real range data with ground truth. From the experimental evaluation results, the proposed methods are shown to be effective, and the general least-squares-based methods are shown to be unsuitable for the assumed noise model.