Due to the high cost of labeling and the high requirements of annotation professionalism, there is a lack of labeling of large quantities of data. As a solution to the problem of partially labeled data in federated learning (FL), federated semi-supervised learning (FSSL) has emerged. To take advantage of this large volume of unlabeled data to improve model performance, we propose a semi-supervised federated learning (TGAFed) based on truncated Gaussian aggregation, which focuses on the case where each client has access to both labeled and unlabeled data in the federated semi-supervised learning. The unlabeled samples were weighted according to the truncated Gaussian distribution fitted by the model prediction probability of the unlabeled samples, so as to optimize the filtering of pseudo-label and generates a new inter-client consistency loss based on truncated Gaussian distribution to improve the utilization rate of pseudo-label. Then, clients perform mean aggregation based on local quantity-quality factors, while global quantity-quality factors assist clients in their local updates through exponential moving averages, gradually improving the performance of the global model. Finally, we validate the superiority of the TGAFed method on three benchmark datasets, Cifar100, Cifar10 and CINIC-10.