By using inter-class and intra-class K-Nearest Neighbors (KNNs), weighted twin support vector machine (WLTSVM) mines as much potential similarity information in samples as possible to improve the common short-coming of nonparallel hyperplane classifiers. Multi-view learning (MVL) has a lot of potential due to the multi-modal datasets that are becoming available. In this paper, we propose a new multi-view learning with privileged weighted twin support vector machine (MPWTSVM). It not only inherits the advantages of WLTSVM but also has its characteristics. Firstly, it enhances generalization ability by mining intra-class information from the same perspective. Secondly, it reduces the redundant constraints with the help of inter-class information, thus improving the running speed. Most importantly, it can follow both the consensus and the complementary principles simultaneously. The consensus principle is realized by minimizing the coupling items of different views in the original objective function. The complementary principle is achieved by establishing privileged information paradigms and MVL. Compared with state-of-the-art MVL methods: SVM-2K, MVTSVM, MCPK, PSVM-2V, MVRDTSVM and MVTHSVM-2C, our model has better accuracy and classification efficiency. Experimental results on numerous datasets prove the effectiveness of the proposed algorithm. •A new multi-view classification method (MPWTSVM) is proposed.•MPWTSVM follows both the consensus and the complementary principle.•MPWTSVM enhances generalization ability by mining intra-class information.•MPWTSVM reduces the redundancy constraints by inter-class information.•MPWTSVM establishes privileged information paradigms.