Sequential recommendation effectively addresses information overload by modeling users' temporal and sequential interaction patterns. To overcome the limitations of supervision signals, recent approaches have adopted self-supervised learning techniques in recommender systems. However, there are still two critical challenges that remain unsolved. Firstly, existing sequential models primarily focus on long-term modeling of individual interaction sequences, overlooking the valuable short-term collaborative relationships among the behaviors of different users. Secondly, real-world data often contain noise, particularly in users' short-term behaviors, which can arise from temporary intents or misclicks. Such noise negatively impacts the accuracy of both graph and sequence models, further complicating the modeling process. To address these challenges, we propose a novel framework called Self-Supervised Graph Neural Network (SelfGNN) for sequential recommendation. The SelfGNN framework encodes short-term graphs based on time intervals and utilizes Graph Neural Networks (GNNs) to learn short-term collaborative relationships. It captures long-term user and item representations at multiple granularity levels through interval fusion and dynamic behavior modeling. Importantly, our personalized self-augmented learning structure enhances model robustness by mitigating noise in short-term graphs based on long-term user interests and personal stability. Extensive experiments conducted on four real-world datasets demonstrate that SelfGNN outperforms various state-of-the-art baselines. Our model implementation codes are available at https://github.com/HKUDS/SelfGNN.