This paper studies the simultaneous localization and mapping (SLAM) algorithm based on the extended Kalman filter (EKF-SLAM) to achieve the navigation positioning of underwater gliders in the three-dimensional space, as well as to estimate the position of acoustic beacons which are used to measure distances as gliders move. The model of SLAM system consists of two parts: one part is the glider model, calculating the three-dimensional kinematic characteristics of the glider, expanding with the current velocity, and the other part is the beacon model, in order to reckon the planar coordinates of three acoustic beacons without a prior known positions. Based on measurements of distances between the glider and beacons, the position of glider and beacons can be estimated synchronously, utilizing the EKF method. Since the glider runs more than one cycle, the estimation of states in EKF-SLAM system can be optimized, combining with measured location of the glider at the sea surface gained by the global positioning system (GPS). The simulation results indicate that the EKF-SLAM algorithm for glider positioning is correct and effective, which also has high location accuracy.978-1-4799-8730-6/15/$31.00