The motion capture system that supports full-body virtual representation is of key significance for virtual reality. Compared to vision-based systems, full-body pose estimation from sparse tracking signals is not limited by environmental conditions or recording range. However, previous works either face the challenge of wearing additional sensors on the pelvis and lower-body or rely on external visual sensors to obtain global positions of key joints. To improve the practicality of the technology for virtual reality applications, we estimate full-body poses using only inertial data obtained from three Inertial Measurement Unit (IMU) sensors worn on the head and wrists, thereby reducing the complexity of the hardware system. In this work, we propose a method called Progressive Inertial Poser (ProgIP) for human pose estimation, which combines neural network estimation with a human dynamics model, considers the hierarchical structure of the kinematic chain, and employs a multi-stage progressive network estimation with increased depth to reconstruct full-body motion in real time. The encoder combines Transformer Encoder and bidirectional LSTM (TE-biLSTM) to flexibly capture the temporal dependencies of the inertial sequence, while the decoder based on multi-layer perceptrons (MLPs) transforms high-dimensional features and accurately projects them onto Skinned Multi-Person Linear (SMPL) model parameters. Quantitative and qualitative experimental results on multiple public datasets show that our method outperforms state-of-the-art methods with the same inputs, and is comparable to recent works using six IMU sensors.