Chronic ankle instability (CAI) is a major public health concern and adversely affects people's mobility and quality of life. Traditional assessment methods are subjective and qualitative by means of clinician observation and patient self-reporting, which may lead to inaccurate assessment and reduce the effectiveness of treatment in clinical practice. Gait analysis becomes a commonly used approach for monitoring human motion behaviors, which can be applied to specific diagnosis and assessment of CAI. However, it is still challenging to recognize the pathological gait pattern for CAI subjects. In this paper, we propose an integrated deep learning framework to solve the CAI recognition problem using kinematic data. Specifically, inspired by the biomechanics of human body system, we create a simple graph neural network (GNN), termed GaitNet, that operates on a spatial domain and exploits interactions among 3-D joint coordinates. We also develop an attention reinforcement learning (ARL) model that determines attention weights of frames on a temporal domain, which is combined with GaitNet for prediction. The effectiveness of our method is validated on the kinematic NEU-CAI dataset which is collected in our institution using a stereophotogrammetric system. According to extensive experiments, we demonstrate that the selected key phases (i.e., sequences of frames with high attentions) significantly increase the predictability of the proposed biomechanics-based GNN model to differentiate between CAI cohort and control cohort. Moreover, we show a significant prediction accuracy improvement (20%-25%) by our approach compared to state-of-the-art machine learning and deep learning methods.