Abstract: In order to solve the large computing cost and numerical instabilities of simultaneous localization and mapping (SLAM), a square root cubature Kalman filter (SRCKF) based SLAM algorithm (SRCKF-SLAM) for mobile robots is designed according to cubature Kalman filter (CKF) principle. The SRCKF-SLAM algorithm accomplishes prediction and observation through motion model and observation model, and it is updated iteratively by propagating square root factors of the mean and covariance of the state variable, which guarantees the symmetry and positive semi-definiteness of the covariance matrix and therefore improves numerical accuracy and stability. The simulation experiments show that, compared with the CKF-SLAM algorithm, the root-mean square error of the SRCKF-SLAM algorithm decreases 14%, and the percentage of points in consistency area increases 36%, therefore the SRCKF-SLAM algorithm effectively satisfies the requirement of SLAM navigation of mobile robots.