Learning from data sequentially arriving, possibly in a non i.i.d. way, with changing task distribution over time is called continual learning. Much of the work thus far in continual learning focuses on supervised learning and some recent works on unsupervised learning. In many domains, each task contains a mix of labelled (typically very few) and unlabelled (typically plenty) training examples, which necessitates a semi-supervised learning approach. To address this in a continual learning setting, we propose a framework for semi-supervised continual learning called Meta-Consolidation for Continual Semi-Supervised Learning (MCSSL). Our framework has a hypernetwork that learns the meta-distribution that generates the weights of a semi-supervised auxiliary classifier generative adversarial network $(\textit{Semi-ACGAN})$ as the base network. We consolidate the knowledge of sequential tasks in the hypernetwork, and the base network learns the semi-supervised learning task. Further, we present $\textit{Semi-Split CIFAR-10}$, a new benchmark for continual semi-supervised learning, obtained by modifying the $\textit{Split CIFAR-10}$ dataset, in which the tasks with labelled and unlabelled data arrive sequentially. Our proposed model yields significant improvements in the continual semi-supervised learning setting. We compare the performance of several existing continual learning approaches on the proposed continual semi-supervised learning benchmark of the Semi-Split CIFAR-10 dataset.