Subspace clustering has important and wide applications in computer vision and pattern recognition. It is a challenging task to learn low-dimensional subspace structures due to complex noise existing in high-dimensional data. Complex noise has much more complex statistical structures, and is neither Gaussian nor Laplacian noise. Recent subspace clustering methods usually assume a sparse representation of the errors incurred by noise and correct these errors iteratively. However, large corruptions incurred by complex noise cannot be well addressed by these methods. A novel optimization model for robust subspace clustering is proposed in this paper. Its objective function mainly includes two parts. The first part aims to achieve a sparse representation of each high-dimensional data point with other data points. The second part aims to maximize the correntropy between a given data point and its low-dimensional representation with other points. Correntropy is a robust measure so that the influence of large corruptions on subspace clustering can be greatly suppressed. An extension of pairwise link constraints is also proposed as prior information to deal with complex noise. Half-quadratic minimization is provided as an efficient solution to the proposed robust subspace clustering formulations. Experimental results on three commonly used data sets show that our method outperforms state-of-the-art subspace clustering methods.