Aiming at the problem of modeling for non-equidistant sequence, the non-equidistant GM(1,1) power model was proposed. A non-linear optimization model is constructed with the objective of minimum average relative error, the constraints of relationships between parameters in order to optimize the power exponent and the background value. The results showed that the form of non equidistant GM(1,1) power model was more flexible than the traditional ones. Both non equidistant GM(1,1) model and Grey Verhulst model were the special cases of non equidistant GM(1,1) power model. Optimization of power exponent helped to improve modeling accuracy. Finally, an engineering example of non-equidistant sequence shows modeling accuracy in traditional modeling, which was significantly improved by non equidistant GM(1,1) power model.