Unsupervised feature selection attracts much attention in the field of machine learning, and is very important for dimensionality reduction and classification of high-dimensional data. The similarity between data points can be measured by several different criteria, which results in the inconsistency of the similarity measure criteria between different data points. At the same time, in existing methods, the similarity matrices are most obtained by allocation of neighbors, so that the number of the connected components is usually not ideal. To address the two problems, a Self-Adaptive Multi-measure unsupervised feature selection with Structured Graph Optimization (SAM-SGO) method was proposed with regarding the similarity matrix as a variable instead of a preset thing. By fusing different measure functions into a unified measure adaptively, various measure methods could be synthesized, the similarity matrix of data was obtained adaptively, and the relationships between data points were captured more accurately. In order to obtain an ideal graph structure, a constraint was imposed on the rank of similarity matrix to optimize the local structure of the graph and simplify the calculation. In addition, the graph based dimensionality reduction problem was incorporated into the proposed adaptive multi-measure problem, and the sparsity-inducing l _2,0 regularization constraint was introduced to obtain the sparse projection used for feature selection. Experiments on several standard datasets demonstrate the effectiveness of SAM-SGO. Compared with Local Learning-based Clustering Feature Selection (LLCFS), Dependence Guided Unsupervised Feature Selection (DGUFS) and Structured Optimal Graph Feature Selection (SOGFS) methods proposed in recent years, the clustering accuracy of this method is improved by about 3.6 percentage points averagely.