As linear dimensionality reduction methods usually cannot produce satisfactory low-dimensional embedding when applied to data with nonlinear structure, a new nonlinear dimensionality reduction method named NNSE was proposed to keep the local nearest neighbor information in the high-dimensional space. Firstly, the nearest neighbor points were found by calculating the Euclidean distance between the sample points in the high-dimensional space, then a random initial distribution of the data points was generated in the low-dimensional space. Secondly, by moving the data points towards the mean position of their nearest neighbors found in the high-dimensional space, the data point positions were iteratively optimized until the embedding becomes stable. In the comparison with a state-of-the-art nonlinear stochastic dimensionality reduction method named t-SNE (t-distributed Stochastic Neighbor Embedding), the low-dimensional embedding produced by NNSE method is similar to the visualization produced by the t-SNE method. However, it is shown that the NNSE method is superior to t-SNE in preserving the local nearest neighbor information in the low-dimensional embedding by using a quantitative indicator.