In this paper, some mathematical tools were used to solve the system forecasting problems of a class of data changing in leaps and bounds at a certain point.And combined with an economic forecasting exam-ple and theoretical derivation, a method to predict some systems that can not use existing prediction methods was put forward.The new method fits initial function with grey model and map prediction with the neutral functional differential equations, and makes good pre-measured to the example, which is hard to be solved by the conven-tional forecasting method.%利用数学工具来解决一类数据在某一点处出现跳跃性变化的系统预测问题。并结合一个经济预测实例，对某种不能用已有预测方法预测的系统，经理论推导，提出了一种以灰色模型拟合初值函数，以中立型泛函微分方程映射预测的预测方法，对实例做出了良好的预测，解决了用常规预测方法难以解决的问题。
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