In this paper, we propose a method about task scheduling and data assignment on heterogeneous hybrid memory multiprocessor systems for real-time applications. In a heterogeneous hybrid memory multiprocessor system, an important problem is how to schedule real-time application tasks to processors and assign data to hybrid memories. The hybrid memory consists of dynamic random access memory and solid state drives when considering the performance of solid state drives into the scheduling policy. To solve this problem, we propose two heuristic algorithms called improvement greedy algorithm and the data assignment according to the task scheduling algorithm, which generate a near-optimal solution for real-time applications in polynomial time. We evaluate the performance of our algorithms by comparing them with a greedy algorithm, which is commonly used to solve heterogeneous task scheduling problem. Based on our extensive simulation study, we observe that our algorithms exhibit excellent performance and demonstrate that considering data allocation in task scheduling is significant for saving energy. We conduct experiments on two heterogeneous multiprocessor systems.Given a heterogeneous hybrid memory multiprocessor system that consists of n heterogeneous processors P 1 ; P 2 ; : : : ; P n , and each processor P i contains a hybrid memory, which is equipped with DRAM i and SSD i . The access time and access energy of each processor in accessing a unit data In DAA_TS algorithm, we first use the HEFT algorithm to initialize the schedule. And then, we propose Data-Aware Algorithm, which is denoted in Algorithm 3 to find the share data and the single data. The share data and the single data are denoted as share_d and si ngle_d , respectively. We can save much more cost to first assign share_d , because the memory store share_d will be accessed more than once.After identifying the type of data, we propose Data Assignment Algorithm described in Algorithm 4. In Algorithm 4, we build two queues, one is a memory queue denoted as M and other one is a Then, each single data is always placed in the processor to access the fastest and spatial memory. As a result, we draw the tasks and data schedule scheme. However, this result was not the most ideal. In order to satisfy the time constraint and the minimal energy consumption with the resource constraint, the DAA_TS algorithm is also contained in the following optimization algorithm to reduce the energy consumption EC and the completion time T .At first, we change tasks and data position to achieve the energy consumption of minimal mi n_E. And then, the task scheduling and data assignment problem is solved, if the total completion time T satisfies the time constraint S . Otherwise, for reaching the time constraint S requirement, tasks and data should be reallocated. After T < S, we will adopt tasks migration. While reallocating a set of data D, until the energy consumption cannot be reduced any more. Otherwise, we should reallocate some tasks and some data to guarantee the finish time...