The energy consumption is always a serious problem for mobile devices powered by battery. As the capacity and density of off-chip memory continuous to scale, its energy consumption accounts for a considerable amount of the whole system energy. There are therefore strong demands for energy efficient techniques towards memory system. Different from previous works, we explore the different power management modes of the off-chip memory by process scheduling for the multi-core mobile devices. In particular, we schedule the processes based on their memory access characteristics to maximize the number of the memory banks being in low power mode. We propose a fast approximation algorithm to solve the scheduling process problem for the dual-core mobile device. And for those equipped with more than two cores, we prove that the scheduling process problem is NP-Hard, and propose two heuristic algorithms. The proposed algorithms are evaluated through a series of experiments, for which we have encouraging results.