Kinetics data such as ground reaction forces (GRFs) are commonly used as indicators for rehabilitation and sports performance; however, they are difficult to measure with convenient wearable devices. Therefore, researchers have attempted to estimate accurately unmeasured kinetics data with artificial neural networks (ANNs). Because the inputs to an ANN affect its performance, they must be carefully selected. The GRF and center of pressure (CoP) have a mechanical relationship with the center of mass (CoM) in the three dimensions (3D). This biomechanical characteristic can be used to establish an appropriate input and structure of an ANN. In this study, an ANN for estimating gait kinetics with a single inertial measurement unit (IMU) was designed; the kinematics of the IMU placed on the sacrum as a proxy for the CoM kinematics were applied based on the 3D spring mechanics. The walking data from 17 participants walking at various speeds were used to train and validate the ANN. The estimated 3D GRF, CoP trajectory, and joint torques of the lower limbs were reasonably accurate, with normalized root-mean-square errors (NRMSEs) of 6.7% to 15.6%, 8.2% to 20.0%, and 11.4% to 24.1%, respectively. This result implies that the biomechanical characteristics can be used to estimate the complete three-dimensional gait data with an ANN model and a single IMU.