Human motion capture with sparse inertial sensors has gained significant attention recently. However, existing methods almost exclusively rely on a template adult body shape to model the training data, which poses challenges when generalizing to individuals with largely different body shapes (such as a child). This is primarily due to the variation in IMU-measured acceleration caused by changes in body shape. To fill this gap, we propose Shape-aware Inertial Poser (SAIP), the first solution considering body shape differences in sparse inertial-based motion capture. Specifically, we decompose the sensor measurements related to shape and pose in order to effectively model their joint correlations. Firstly, we train a regression model to transfer the IMU-measured accelerations of a real body to match the template adult body model, compensating for the shape-related sensor measurements. Then, we can easily follow the state-of-the-art methods to estimate the full body motions of the template-shaped body. Finally, we utilize a second regression model to map the joint velocities back to the real body, combined with a shape-aware physical optimization strategy to calculate global motions on the subject. Furthermore, our method relies on body shape awareness, introducing the first inertial shape estimation scheme. This is accomplished by modeling the shape-conditioned IMU-pose correlation using an MLP-based network. To validate the effectiveness of SAIP, we also present the first IMU motion capture dataset containing individuals of different body sizes. This dataset features 10 children and 10 adults, with heights ranging from 110 cm to 190 cm, and a total of 400 minutes of paired IMU-Motion samples. Extensive experimental results demonstrate that SAIP can effectively handle motion capture tasks for diverse body shapes. The code and dataset are available at https://github.com/yinlu5942/SAIP.