Multiview subspace clustering, which aims to cluster the given data points with information from multiple sources or features into their underlying subspaces, has a wide range of applications in the communities of data mining and pattern recognition. Compared with the single-view subspace clustering, it is challenging to efficiently learn the structure of the representation matrix from each view and make use of the extra information embedded in multiple views. To address the two problems, a novel correntropy-based multiview subspace clustering (CMVSC) method is proposed in this article. The objective function of our model mainly includes two parts. The first part utilizes the Frobenius norm to efficiently estimate the dense connections between the points lying in the same subspace instead of following the standard compressive sensing approach. In the second part, the correntropy-induced metric (CIM) is introduced to characterize the noise in each view and utilize the information embedded in different views from an information-theoretic perspective. Furthermore, an efficient iterative algorithm based on the half-quadratic technique (HQ) and the alternating direction method of multipliers (ADMM) is developed to optimize the proposed joint learning problem, and extensive experimental results on six real-world multiview benchmarks demonstrate that the proposed methods can outperform several state-of-the-art multiview subspace clustering methods.