The application of vision-language models (VLMs) has achieved impressive success in various robotics tasks. However, there are few explorations for foundation models used in quadruped robot navigation through terrains in 3D environments. We introduce SARO (Space-Aware Robot System for Terrain Crossing), an innovative system composed of a high-level reasoning module, a closed-loop sub-task execution module, and a low-level control policy. It enables the robot to navigate across 3D terrains and reach the goal position. For high-level reasoning and execution, we propose a novel algorithmic system taking advantage of a VLM, with a design of task decomposition and a closed-loop sub-task execution mechanism. For low-level locomotion control, we utilize the Probability Annealing Selection (PAS) method to effectively train a control policy by reinforcement learning. Numerous experiments show that our whole system can accurately and robustly navigate across several 3D terrains, and its generalization ability ensures the applications in diverse indoor and outdoor scenarios and terrains. Appendix and Videos can be found in project page: https://saro-vlm.github.io/.