In this paper, we propose a method of mobile robot localization based on chirp-spread-spectrum (CSS) ranging. By using the CSS system, the distances between a mobile robot and CSS nodes fixed at known coordinates can be measured according to the time of flight of radio frequency signals. Based on the measured distances, the coordinates of a mobile robot can be calculated by the method of trilateration. To deal with measurement noise, an extended Kalman filter (EKF) can be applied to estimate the coordinate of the mobile robot. These measured distances, however, are not only noisy but also biased. Therefore, the estimated coordinates of the mobile robot represent inconsistent values. To solve the problem of bias, we define a scaling factor, which corresponds to the change of the magnitude of a measured distance vector that is due to biases. Based on the scaling factor, we develop a new biased measurement model and apply the EKF to our model for estimating the coordinates of a mobile robot. Through localization experiments, we evaluate the performance of the proposed algorithm.