Fairness of recommender systems (RS) has attracted increasing attention recently. Based on the involved stakeholders, the fairness of RS can be divided into user fairness, item fairness, and two-sided fairness which considers both user and item fairness simultaneously. However, we argue that the intersectional two-sided unfairness may still exist even if the RS is two-sided fair, which is observed and shown by empirical studies on real-world data in this paper, and has not been well-studied previously. To mitigate this problem, we propose a novel approach called Intersectional Two-sided Fairness Recommendation (ITFR). Our method utilizes a sharpness-aware loss to perceive disadvantaged groups, and then uses collaborative loss balance to develop consistent distinguishing abilities for different intersectional groups. Additionally, predicted score normalization is leveraged to align positive predicted scores to fairly treat positives in different intersectional groups. Extensive experiments and analyses on three public datasets show that our proposed approach effectively alleviates the intersectional two-sided unfairness and consistently outperforms previous state-of-the-art methods.