To overcome the system errors of the grey GM(1,1) power model, in which the parameters estimation is discrete and the forecast function is continuous, a new fractional order grey discrete GM(1,1) power model is constructed, and the method of regularization is used in stead of the least square method in some parameters' estimation because of the problem of ill-condition to improve the accuracy of parameters estimation. A new method is proposed to determine the optimization values of accumulation order and power exponential so as to increase the forecast precision. The tests on the forecast of industrial waste emissions rate and urban water consumption show that the proposed model and the methods of parameters estimation have higher forecast accuracy in oscillation sequences.