In a multi-label learning problem, each instance is associated with multiple labels simultaneously. However, problem becomes more complicated when labels are missing. Many multi-label based real-life applications, such as medical diagnosis, protein function prediction, image annotations are framed as networks which are used to model interactions between complex entities. Although, in many scenarios these interactions may not be pairwise, rather should described as higher-order interactions. For such a scenario Hypergraphs are preferred rather than simple Laplacian. Multilabel twin support vector machines (MLTSVM) has become popular due its performance for multilabel classification. In this paper, to deal with missing label scenario, we propose a semi-supervised framework termed as Hypergraph Least Squares Twin Support Vector Machine for Multi-label Learning (HMLLSTSVM) wherein we have used Hypergraph Laplacian to train our classifier utilizing both labeled and unlabeled samples. We incorporate the idea of Hypergraph along with least squares loss function into MLTSVM, which improves the efficacy in terms of classification accuracy and speed of our proposed model. Taking motivation from KNN-based Least Squares Twin Support Vector Machine (KNNLSTSVM), we have incorporated the intrinsic similarity information among the samples in our proposed model’s objective function, which makes our classifier HMLLSTSVM less sensitive to outliers. Experimental results on benchmark multilabel datasets proves the efficacy of the classifier.