Combined computation and communication workload mapping and scheduling pose a major challenge in embedded NoC-based MPSoC design. While contemporary researches largely focus on data locality-centric mapping methodologies, unawareness of transmission route and timing may negatively impact the mapping efficiency. In this paper, we develop a unified communication-aware NoC-based MPSoC mapping and scheduling algorithm, in which a list-scheduling method is used to map prioritized tasks to the best fit processor, based on a transmission route-aware cost function. Our algorithm is able to realize precise and predictable packet routing in the process of task mapping, and achieve shorter end-to-end application execution time. To evaluate our algorithm, we conduct experiments using three real applications on a simulated NoC-based MPSoC platform. Comparison results show that our algorithm can achieve greatly improved overall end-to-end time, and about 38.3% less transmission time on a 3 x 3 mesh structure.