The gray prediction theory has already been widely applied to solving all kinds of social, scientific and technical problems. It is also used for the prediction of engineering mechanical and material scientific problems. But the traditional gray prediction model is applicable only for equidistant time sequences. In order to extend the scope of application, an improved gray prediction model is put forward. By weighted summation, the new developed gray prediction model can also be applied to the situation of non-equidistant time sequence. The improved gray prediction model is used for the prediction of creep fracture time of rocks and gypsum. The deduced results are proven to be very accurate. The research work of the current paper opens many opportunities for further thoughts of the prediction of many other engineering mechanical problems.