Visualization is an important method in microbiome data analysis, and dimensionality reduction is a necessary procedure to achieve it. Multidimensional Scaling (MDS) is a popular method, which is necessary to compute the distance matrix. The Unifrac distance is very reasonable and biologically meaningful in the analysis of microbiome data. Due to the complexity of the phylogenetic tree and the high dimensionality of data, MDS needs a large amount of calculations to determine all the distances between pairs. In this paper, we proposed a novel dimensionality reduction algorithm based on Laplace matrix (DRLM) for the analysis of microbiome data. The experimental results indicate that both on synthesized and microbiome data, our algorithm DRLM can not only cluster the data more clearly, but also can significantly reduce the computational cost.