Graph-based methods have achieved impressive performance on semisupervised classification (SSC). Traditional graph-based methods have two main drawbacks. First, the graph is predefined before training a classifier, which does not leverage the interactions between the classifier training and similarity matrix learning. Second, when handling high-dimensional data with noisy or redundant features, the graph constructed in the original input space is actually unsuitable and may lead to poor performance. In this article, we propose an SSC method with novel graph construction (SSC-NGC), in which the similarity matrix is optimized in both label space and an additional subspace to get a better and more robust result than in original data space. Furthermore, to obtain a high-quality subspace, we learn the projection matrix of the additional subspace by preserving the local and global structure of the data. Finally, we intergrade the classifier training, the graph construction, and the subspace learning into a unified framework. With this framework, the classifier parameters, similarity matrix, and projection matrix of subspace are adaptively learned in an iterative scheme to obtain an optimal joint result. We conduct extensive comparative experiments against state-of-the-art methods over multiple real-world data sets. Experimental results demonstrate the superiority of the proposed method over other state-of-the-art algorithms.