Grey prediction mainly concerns uniform distribution interval grey number prediction recently. A grey prediction model of normal distribution interval grey number sequence is developed, based on grey hazy set evolutionary thinking and normal distribution which is the main existence way of uncertain information. Firstly, the information equivalence conversion between interval grey number and real numbers sequence family is achieved by using the normal distribution random function. Then, the GM(1,1) model of random sequences on the normal distribution interval grey number is given, the interval grey number prediction model is established by using maximum minimum values and the normal distribution “three sigma rule”. Through the example comparative analysis, the results show that the model is feasible and effective, providing new ideas and models for the interval grey number prediction.