In view of the demand for impact point prediction of ballistic missiles in precise guidance after large-scale maneuver penetration， an analytical missile impact point prediction model that considers the influence of high-order disturbing gravity is proposed. The impact point prediction problem is decomposed into two parts： Standard impact point prediction and impact point deviation prediction. The standard impact point prediction is directly solved by the two-body orbit theory， and the impact point deviation prediction is solved by the constructed state space perturbation model. The spherical harmonics pole-changing method is used to establish the expression of the high-order disturbing gravity vector in the orbit cylindrical coordinate system， and the analytical model for impact point deviation prediction composed of two types of kernel functions， such as F function and G function， is then derived， as well as the recursive formulas of F function and G function. This model does not require pre-launching preparations， and is more flexible in use and more robust than the existing methods. Numerical simulation results show that the average residual error of the impact point prediction model proposed in this paper is 11.2 m， the relative error is less than 0.1%， and the prediction time is less than 100 ms. It can provide support for the design of guidance algorithms and has certain engineering application value.