High Performance ParalleX (HPX) is one of taskbased programming and execution models, which provides a C++ class library to describe tasks and their dependencies, and also a runtime system for task-based distributed-memory parallel computing. In the original HPX mechanism, the execution of some critical tasks might be delayed by executing other noncritical tasks. This paper hence proposes to incorporate task priority control into the HPX runtime system. First, this paper discusses use of multiple thread pools to prioritize critical tasks. The waiting time of critical tasks is reduced by assigning critical tasks to a dedicated thread pool that is different from the thread pool for non-critical tasks. Second, this paper discusses how to assign worker threads to processor cores. A different number of worker threads are associated with each thread pool, and then mapped to processor cores so as to mitigate the load imbalance among the NUMA domains. In this paper, the performance of the proposed mechanism is evaluated using two task-based applications and three different scales of NUMA systems. The evaluation results clearly demonstrate that the proposed mechanism can improve the performance of HPX applications by successfully prioritizing critical tasks and also reducing the load imbalance of the NUMA domains.