A new motion-free iterative closest point (ICP) algorithm is proposed for building a two-dimensional (2D) map for mobile robot navigation. A laser range finder (LRF) sensor is installed on a mobile robot to scan and measure the depth data of the environment to form a 2D map during mobile robot navigation. Because the scanning and navigation motions are performed independently, the scanned data contain distortions from the motions of the mobile robot. To compensate for the distortions, the proposed motion-free ICP algorithm estimates the effects of the dynamic motions of the robot on the scanning process. That is, the motion-free algorithm compensates for the distance measurement errors related to the dynamic changes in the mobile robot's velocity. Experiments were performed with actual velocity changes of a mobile robot to demonstrate and verify the effective performance of the proposed algorithm.