We propose a novel, adaptive, and general framework for federate semi-supervised learning, which is a new research paradigm aiming to exploit the power of unlabeled data ignored by existing federated supervised learning. Introducing unlabeled data to federated learning brings several new challenges, which limits the applicability of existing models. In this proposal, we define the federated semi-supervised learning problem from the insight of data regularization and analyze the new-raised difficulties. In particular, we propose a novel learning framework, named FedSemi, to introduce the consistency regularization technique into federated learning using a teacher-student model in Task 1. In Task 2, we further propose a new metric to measure the divergence of local model layers. Using the divergence, FedSemi can automatically select layer-level parameters to be uploaded to the server in an adaptive manner. In Task 3, we propose an element-wise aggregation approach to reduce the influence of the noisy gradients in the global model aggregation. Task 4 aims to evaluate the proposed framework on three different real-world applications, including image classification, sentiment analysis, and health prediction. This project creates new fundamental knowledge in both federated learning and semisupervised learning fields and will significantly advance these two fields by developing novel methods and implementing analytic tools.