In general, three-dimensional ground reaction forces (GRFs) and ground reaction moments (GRMs) that occur during human gait are measured using a force plate, which are expensive and have spatial limitations. Therefore, we proposed a prediction model for GRFs and GRMs, which only uses plantar pressure information measured from insole pressure sensors with a wavelet neural network (WNN) and principal component analysis-mutual information (PCA-MI). For this, the prediction model estimated GRFs and GRMs with three different gait speeds (slow, normal, and fast groups) and healthy/pathological gait patterns (healthy and adolescent idiopathic scoliosis (AIS) groups). Model performance was validated using correlation coefficients (r) and the normalized root mean square error (NRMSE%) and was compared to the prediction accuracy of the previous methods using the same dataset. As a result, the performance of the GRF and GRM prediction model proposed in this study (slow group: r = 0.840–0.989 and NRMSE% = 10.693–15.894%; normal group: r = 0.847–0.988 and NRMSE% = 10.920–19.216%; fast group: r = 0.823–0.953 and NRMSE% = 12.009–20.182%; healthy group: r = 0.836–0.976 and NRMSE% = 12.920–18.088%; and AIS group: r = 0.917–0.993 and NRMSE% = 7.914–15.671%) was better than that of the prediction models suggested in previous studies for every group and component (*p* < 0.05 or 0.01). The results indicated that the proposed model has improved performance compared to previous prediction models.