Sequential recommendation approaches have demonstrated remarkable proficiency in modeling user preferences. Nevertheless, they are susceptible to profile pollution attacks (PPA), wherein items are introduced into a user's interaction history deliberately to influence the recommendation list. Since retraining the model for each polluted item is time-consuming, recent PPAs estimate item influence based on gradient directions to identify the most effective attack candidates. However, the actual item representations diverge significantly from the gradients, resulting in disparate outcomes.To tackle this challenge, we introduce an INFluence Function-based Attack approach INFAttack that offers a more accurate estimation of the influence of polluting items. Specifically, we calculate the modifications to the original model using the influence function when generating polluted sequences by introducing specific items. Subsequently, we choose the sequence that has been most significantly influenced to substitute the original sequence, thus promoting the target item. Comprehensive experiments conducted on five real-world datasets illustrate that INFAttack surpasses all baseline methods and consistently delivers stable attack performance for both popular and unpopular items.