Heterogeneous multi-core platforms, such as ARM big.LITTLE are widely used to execute embedded applications under multiple and contradictory constraints, such as energy consumption and real-time execution. To fulfill these constraints and optimize system performance, application tasks should be efficiently mapped on multi-core platforms. Embedded applications are usually tolerant to approximated results but acceptable Quality-of-Service (QoS). Modeling embedded applications by using the elastic task model, namely, Imprecise Computation (IC) task model, can balance system QoS, energy consumption, and real-time performance during task deployment. However, stateof-the-art approaches seldom consider the problem of IC task deployment on heterogeneous multi-core platforms. They typically neglect task migration, which can improve the solutions due to its flexibility during the task deployment process. This paper proposes a novel QoS-aware task deployment method to maximize system QoS under energy and real-time constraints, where frequency assignment, task allocation, scheduling, and migration are optimized simultaneously. The task deployment problem is formulated as mixed-integer non-linear programming. Then, it is linearized to mixed-integer linear programming to find the optimal solution. Furthermore, based on problem structure and problem decomposition, we propose a novel heuristic with low computational complexity. The sub-problems regarding frequency assignment, task allocation, scheduling, and adjustment are considered and solved in sequence. Finally, the simulation results show that the proposed task deployment method improves the system QoS by 31.2% on average (up to 112.8%) compared to the state-of-theart methods and the designed heuristic achieves about 53.9% (on average) performance of the optimal solution with a negligible computing time.