Ground vibrations induced by underground mining blasting has a significant impact on the stability and safety of surface buildings near mines. Due to the thick rock layers overlying underground mines, there is presently limited accuracy in regard to predicting ground vibrations induced by underground mine blasting. Therefore, this study aims to improve the accuracy of predicting ground vibrations induced by underground blasting by comprehensively measuring the peak particle velocity (PPV) in all three directions and independently considering on the impact of vertical distance. Random forest regression (RFR), bagging regression (BR), and gradient boosting regression (GBR) were used to regress the X-axis PPV (X-PPV), Y-axis PPV (Y-PPV), and Z-axis PPV (Z-PPV) based on blasting records measured at an iron mine. In addition, a genetic algorithm, gray wolf optimizer (GWO), and a particle swarm optimization were used to optimize the parameters of the RFR, BR, and GBR. The comparison results show that GWO-GBR is the optimal model for the prediction of the X-PPV (R2 = 0.8072), Y-PPV (R2 = 0.9147), and Z-PPV (R2 = 0.9265), respectively. Thus, the GWO-GBR model proposed in this study is considered a highly reliable model for predicting ground vibrations induced by underground mine blasting to ensure the safety of the mines’ surroundings.