In this paper, we propose a new technique for path-following of the wheeled mobile robot systems with nonholonomic constraints using a path-observer. We discuss the path-following problems of the nonholonomic mobile robot systems which have two nonsteerable, independently driven wheels with the various initial conditions such as a position, a heading angle, and a velocity. It is shown that the performance of dynamic path-following importantly is affected by the intial conditions. Particularly, if the initial conditions become more distant from the desired path and the desired velocity become faster, the system is shown to have worse performance and small time local stable. To find the controllable and stable control for path-following with various initial configuration, we propose the path-observer which can be used for control of the stable path-following of nonholonomic mobile robot system with the various initial conditions. The proposed scheme exhibits the efficient path-following properties for nonholonomic mobile robot in any intial conditions. The simulation results demonstrate the effectiveness of the proposed method for dynamic path-following tasks with the various initial conditions.