Due to the topology-preserving nature, the SOM(self-organizing map)algorithm can be used to visualize the high-dimensional data. However, due to the fixed regular lattice of neurons, the distance information between the data is lost, and thus the structure of the data may often appear in a distorted form. In order for the map to visualize the structure of the data more naturally, the distance information or the similarity information between the data should be preserved as much as possible on the map directly through the positions of the neurons, along with the topology. To do this, the positions of the neurons should be adjustable on the map. In this paper, a novel position-adjustable SOM algorithm, i.e., DPSOM (distance-preserving SOM), is proposed, which can adaptively adjust the positions of the neurons on the map according to the corresponding distances in the data space and thus can visualize the structure of the data naturally. What's more, the DPSOM algorithm can automatically avoid the excess contraction of the neurons without any additional parameter, thus greatly improving the controllability of the algorithm, and the quality of data visualization.