Clustering plays an essential role in machine learning and data mining. Many real-world datasets for clustering are often different but related in the big data era. Recent research suggests that the individual performance of each learning task could be significantly improved by appropriately transferring knowledge among the related tasks. However, traditional clustering methods, which is limited to a single task, often ignore the correlation between multiple clustering tasks. Multi-task clustering (MTC) has attracted widespread interest recently by attempting to mine sufficient knowledge within multiple related tasks. Existing MTC methods still have the following limitations: 1) the intrinsic geometry of data is seldom considered; 2) the discriminative low-dimensional representation of data is not well explored; 3) the cluster structure of data is neglected in the process of clustering. In order to tackle the above issues, we propose a novel end-to-end Local Learning-based Multi-task Clustering (LLMC) method, which can simultaneously explore discriminative information in a low-dimensional subspace and expose the clustering results for multiple tasks. In particular, the proposed LLMC method can effectively integrate transfer learning, subspace learning, local manifold learning, and clustering. Specifically, a joint projection of heterogeneous features is introduced to control the number of features shared by all the tasks to transfer knowledge among tasks. An efficient iterative algorithm is designed to optimize the objective and is theoretically guaranteed to be convergent. Experimental results demonstrate the superiority of the proposed method over the state-of-the-art single-task and multi-task clustering methods.