In the organization, employees not only need to assume the job responsibilities within the scope of his role, but also need to perform tasks that are not part of his own job, that is, illegitimate tasks. However, as a common phenomenon in enterprises, illegitimate tasks have not been widely discussed in the academic community. Based on the cognitive appraisal theory of stress, a dual mediation model of job engagement as result variable was constructed ,which used challenge stressor appraisal as the promoting mechanism and hindrance stressor appraisal as the inhibiting mechanism, and analyzed the moderating role of growth need strength in this model. The research results based on 286 data in two stages show that: on the one hand, illegitimate tasks can promote employees'' job engagement by inducing challenge stressor appraisal; On the other hand, it can inhibit employees'' job engagement by inducing hindrance stressor appraisal; Growth need strength positively moderates the mediating effect of challenge stressor appraisal on the relationship between illegitimate tasks and job engagement, that is, the stronger the mediating effect is when the growth need strength is high;. Growth need strength negatively moderates the mediating effect of hindrance stressor appraisal on the relationship between illegitimate tasks and job engagement, that is, when the growth need strength is high, the mediating effect is weaker. The results of the study confirm that illegitimate tasks have a double-edged sword effect on employees'' job engagement.