Most of the existing multi-view clustering algorithms are performed in the original feature space, and their performance in heavily reliant on the quality of the raw data. Besides, some two-stage strategies cannot achieve ideal results due to the absence of capturing the correlation between views. In view of this, we propose Multi-View K-means with Laplacian Embedding (MVKLE), which is capable of clustering multi-view data in the learned embedding space. Specifically, we employ local structure-preserving dimensionality reduction to obtain the underlying representation of each view, and obtain the clustering results directly through an effective optimization formulation. Experiments on several common multi-view datasets demonstrate the superiority of the proposed method.