The application workloads in modern MPSoC-based embedded systems are becoming increasingly dynamic. Different applications concurrently execute and contend for resources in such systems, which could cause serious changes in the intensity and nature of the workload demands over time. To cope with the dynamism of application workloads at runtime and improve the efficiency of the underlying system architecture, this article presents a hybrid task mapping algorithm that combines a static mapping exploration and a dynamic mapping optimization to achieve an overall improvement of system efficiency. We evaluate our algorithm using a heterogeneous MPSoC system with three real applications. Experimental results reveal the effectiveness of our proposed algorithm by comparing derived solutions to the ones obtained from several other runtime mapping algorithms. In test cases with three simultaneously active applications, the mapping solutions derived by our approach have average performance improvements ranging from 45.9% to 105.9% and average energy savings ranging from 14.6% to 23.5%.