The key factors of pile foundation settlement were explored for the slope under vertical load by using grey relational analysis, and it is found that each factor is in the following descending order by its influence: elastic modulus > slope distance > slope gradient > internal friction angle > cohesion > soil density > poisson's ratio of soil > pile length > pile diameter. In order to optimize the parameters of support vector regression (SVR) model, a novel HGWO-SVR model was proposed by integrating the differential evolution-enhanced gray wolf algorithm (HGWO). Compared with GWO-SVR and GS-SVR models, this model presents obvious advantage in prediction, with high accuracy and minor error. A settlement prediction model for pile foundation of slope was constructed based on HGWO-SVR model, and the prediction results were compared with those values calculated with existing settlement formulas. The results show that the maximum percentage error between the prediction value of HGWO-SVR model and the calculated value is 6.55%, thus verifying that this model is feasible in settlement prediction for pile foundation of slope.