This paper presents a method with dynamic density topological structure generation for low-cost real-time vertical ladder detection from 3D point cloud data. Dynamic Density Growing Neural Gas (DD-GNG) is proposed to generate a dynamic density of the topological structure. The density of the structure and the number of nodes will be increased in the targeted object area. Feature extraction model is required to classify suspected objects for being processed in the next time process. After that, rungs of the vertical ladder is processed using an inlier-outlier method. Thus, the ladder detection model represents the ladder with a set of nodes and edges. Next, affordance detection is processed for detecting the feasible grasped location. To validate the effectiveness of the proposed method, a series of experiments are conducted on a 4-legged robot with a non-GPU board for real-time vertical ladder detection and climbing to validate the effectiveness of the proposed method. Results show that our proposed method able to detect and track the ladder structure in real-time with a much lower computational cost. The affordance of the ladder provides safety information for robot grasping.