Traffic classification is of great significance for network management, such as improving the quality of service and detecting intrusions. Recently, deep learning-based methods have achieved impressive performance in traffic classification tasks. However, the high cost of data annotation and frequent changes in label definitions often introduce label noise into the training data, which significantly undermines model robustness and generalization. In this work, we propose a robust training framework for building an efficient traffic classifier under label noise to address this problem. First, we introduce Mamba as the backbone of the traffic encoder, since its linear time complexity is suitable for efficient traffic analysis. Then, the Mamba encoder is pre-trained on training data without labels to improve the ability of traffic representation learning. Based on the pre-trained encoder, we build an efficient classifier with a hierarchical feature extraction structure to better adapt to long-sequence traffic in classification. After that, we use a two-component GMM on per-sample losses to split clean and noisy sets. Then, we propose a semi-supervised learning based module to effectively fine-tune the classifier with the two sets of data. The module filters pseudo-labels by confidence and applies contrastive learning to low-confidence samples, avoiding sample discard. Results on three real-world traffic datasets show that our method outperforms state-of-the-art baselines by a large margin across various noise scenarios with superior computational efficiency.