In many practical applications, there are a great number of unlabeled samples available, while labeling them is a costly and tedious process. Therefore, how to utilize unlabeled samples to assist digging out potential information about the problem is very important. In this paper, we study a multiclass semi-supervised classification task in the context of multiview data. First, an optimization method named Parametric multiview semi-supervised classification (PMSSC) is proposed, where the built classifier for each individual view is explicitly combined with a weight factor. By analyzing the weakness of it, a new adapted weight learning strategy is further formulated, and we come to the convex multiview semi-supervised classification (CMSSC) method. Comparing with the PMSSC, this method has two significant properties. First, without too much loss in performance, the newly used weight learning technique achieves eliminating a hyperparameter, and thus it becomes more compact in form and practical to use. Second, as its name implies, the CMSSC models a convex problem, which avoids the local-minimum problem. Experimental results on several multiview data sets demonstrate that the proposed methods achieve better performances than recent representative methods and the CMSSC is preferred due to its good traits.