Class-incremental learning (CIL) aims to learn new classes while retaining previous knowledge. Although pre-trained model (PTM) based approaches show strong performance, directly fine-tuning PTMs on incremental task streams often causes renewed catastrophic forgetting. This paper proposes a Dual-Prototype Network with Task-wise Adaptation (DPTA) for PTM-based CIL. For each incremental learning task, an adapter module is built to fine-tune the PTM, where the center-adapt loss forces the representation to be more centrally clustered and class separable. The dual prototype network improves the prediction process by enabling test-time adapter selection, where the raw prototypes deduce several possible task indexes of test samples to select suitable adapter modules for PTM, and the augmented prototypes that could separate confusable classes are utilized to determine the final result. Experiments on multiple benchmarks show that DPTA consistently surpasses recent methods by 1\% - 5\%. Notably, on the VTAB dataset, it achieves approximately 3\% improvement over state-of-the-art methods. The code is open-sourced in https://github.com/Yorkxzm/DPTA}