The scheduling problem in the microelectronic production process has some characteristics including large scale and complex constraints, such as recipe constraint, Setup time, batch capacity and so on. It is difficult to obtain the optimal solution. For the problem with the objective of minimizing the mean cycle time, this paper proposes an indexes fast prediction based decomposition method (DM-IFP). Firstly, after relaxing the non-preemptive constraint, a surrogate method, i.e., the fast prediction method of operation completion time based on the machine load (CTP-ML), is proposed. Then, a CTP-ML based problem decomposition method is designed to decompose the original problems into several consecutive and overlapped subproblems. A double pheromones based ant colony optimization (ACO) algorithm is proposed to solve the subproblem, in which the CTP-ML is applied to obtain the global scheduling objective of each subpropblem so that the original scheduling problem is optimized. Finally, based on some simulated data with different scale, sufficient computational comparisons are provided between the proposed DM-IFP and some representative algorithms. It is shown that the proposed method generates better results in terms of quality and convergence.