Pre-trained language models (PLMs) that achieve success in applications are susceptible to adversarial attack methods that are capable of generating adversarial examples with minor perturbations. Although recent attack methods can achieve a relatively high attack success rate (ASR), our observation shows that the generated adversarial examples have a different data distribution compared with the original examples. Specifically, these adversarial examples exhibit lower confidence levels and higher distance to the training data distribution. As a result, they are easy to detect using very simple detection methods, diminishing the actual effectiveness of these attack methods. To solve this problem, we propose a Distribution-Aware LoRA-based Adversarial Attack (DALA) method, which considers the distribution shift of adversarial examples to improve attack effectiveness under detection methods. We further design a new evaluation metric NASR combining ASR and detection for the attack task. We conduct experiments on four widely-used datasets and validate the attack effectiveness on ASR and NASR of the adversarial examples generated by DALA on the BERT-base model and the black-box LLaMA2-7b model.