Class-incremental learning (CIL) aims to acquire new classes while conserving historical knowledge incrementally. Despite existing pre-trained model (PTM) based methods performing excellently in CIL, it is better to fine-tune them on downstream incremental tasks with massive patterns unknown to PTMs. However, using task streams for fine-tuning could lead to catastrophic forgetting that will erase the knowledge in PTMs. This paper proposes the Dual Prototype network for Task-wise Adaption (DPTA) of PTM-based CIL. For each incremental learning task, a task-wise 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 highly correlated classes are utilized to determine the final result. Experiments on several benchmark datasets demonstrate the state-of-the-art performance of DPTA. The code will be open-sourced after the paper is published.