Simultaneous localization and mapping (SLAM) is a central and complex problem in robot research community. In SLAM, extended Kalman filter (EKF) implementation is widely used to localize the robot and build the environment map incrementally. In this paper, we propose a strong tracking filter (STF) SLAM algorithm. This algorithm applies STF to deal with the non-linear estimated problem in SLAM instead of EKF. It can make the performance of the nonlinear filter approximate to that of optimal linear Kalman Filter (KF), so it can construct high accuracy maps and locate the robot more accurately than EKF SLAM. Simulation experiments illustrate the superior performance of our approach compared to EKF SLAM algorithm.