Pre-trained transformers are popular in state-of-the-art dialogue generation (DG) systems. Such language models are, however, vulnerable to various adversarial samples as studied in traditional tasks such as text classification, which inspires our curiosity about their robustness in DG systems. One main challenge of attacking DG models is that perturbations on the current sentence can hardly degrade the response accuracy because the unchanged chat histories are also considered for decision-making. Instead of merely pursuing pitfalls of performance metrics such as BLEU, ROUGE, we observe that crafting adversarial samples to force longer generation outputs benefits attack effectiveness—the generated responses are typically irrelevant, lengthy, and repetitive. To this end, we propose a white-box multi-objective attack method called DGSlow. Specifically, DGSlow balances two objectives—generation accuracy and length, via a gradient-based multi-objective optimizer and applies an adaptive searching mechanism to iteratively craft adversarial samples with only a few modifications. Comprehensive experiments on four benchmark datasets demonstrate that DGSlow could significantly degrade state-of-the-art DG models with a higher success rate than traditional accuracy-based methods. Besides, our crafted sentences also exhibit strong transferability in attacking other models.