As an essential part of gait analysis in human walking, the ground reaction force (GRF) can be accurately measured using a force platform. However, a force platform is expensive and difficult to implement in the laboratory. One effective method to estimate the GRF without the force platform is the data-driven approach. Two kinds of data-driven strategies are developed in this paper. The first one uses a back-propagation neural network (BPNN) to directly learn a mapping between measured kinematic data and GRFs, while the second one uses a polynomial instead. A gait test for a healthy testee is conducted to get training data and testing data. The angles and angular velocities of the hip, knee, and ankle are used as input candidates. By comparing the estimation results with different candidate combinations, we find the angles and angular velocities of the hip and knee are sufficient to describe the GRF in both approaches. The trained mappings are also used to estimate the GRF under different walking speeds. The results show that the root mean square errors (RMSE) of the test set of the BPNN-based method is less than that of the polynomial-based method. Thus, the BPNN-based method is more robust and accurate in estimating the GRF.