Accurate training labels are a key component for multi-class medical image segmentation. Their annotation is costly and time-consuming because it requires domain expertise. This work aims to develop a dual-branch network and automatically improve training labels for multi-class image segmentation. Transfer learning is used to train the network and improve inaccurate weak labels sequentially. The dual-branch network is first trained by weak labels alone to initialize model parameters. After the network is stabilized, the shared encoder is frozen, and strong and weak decoders are fine-tuned by strong and weak labels together. The accuracy of weak labels is iteratively improved in the fine-tuning process. The proposed method was applied to a three-class segmentation of muscle, subcutaneous and visceral adipose tissue on abdominal CT scans. Validation results on 11 patients showed that the accuracy of training labels was statistically significantly improved, with the Dice similarity coefficient of muscle, subcutaneous and visceral adipose tissue increased from 74.2% to 91.5%, 91.2% to 95.6%, and 77.6% to 88.5%, respectively (p<0.05). In comparison with our earlier method, the label accuracy was also significantly improved (p<0.05). These experimental results suggested that the combination of the dual-branch network and transfer learning is an efficient means to improve training labels for multi-class segmentation.