The field of adversarial textual attack has significantly grown over the past few years, where the commonly considered objective is to craft adversarial examples (AEs) that can successfully fool the target model. However, the imperceptibility of attacks, which is also essential for practical attackers, is often left out by previous studies. In consequence, the crafted AEs tend to have obvious structural and semantic differences from the original human-written text, making them easily perceptible. In this work, we advocate leveraging multi-objectivization to address such an issue. Specifically, we reformulate the problem of crafting AEs as a multi-objective optimization problem, where the attack imperceptibility is considered as an auxiliary objective. Then, we propose a simple yet effective evolutionary algorithm, dubbed HydraText, to solve this problem. HydraText can be effectively applied to both score-based and decision-based attack settings. Exhaustive experiments involving 44,237 instances demonstrate that HydraText consistently achieves competitive attack success rates and better attack imperceptibility than the recently proposed attack approaches. A human evaluation study also shows that the AEs crafted by HydraText are more indistinguishable from human-written text. Finally, these AEs exhibit good transferability and can bring notable robustness improvement to the target model by adversarial training.