We present an algorithm which can realize 3D stereo vision simultaneous localization and mapping (SLAM) for mobile robot in unknown outdoor environments, which means the 6-DOF motion and a sparse but persistent map of natural landmarks be constructed online only with a stereo camera. In mobile robotics research, we extend FastSLAM 2.0 like stereo vision SLAM with "pure vision" domain to outdoor environments. Unlike popular stochastic motion model used in conventional monocular vision SLAM, we utilize the ideas of structure from motion (SFM) for initial motion estimation, which is more suitable for the robot moving in large-scale outdoor, and textured environments. SIFT features are used as natural landmarks, and its 3D positions are constructed directly through triangulation. Considering the computational complexity and memory consumption,Bkd-tree and Best-Bin-First (BBF) search strategy are utilized for SIFT feature descriptor matching. Results show high accuracy of our algorithm, even in the circumstance of large translation and large rotation movements.