Cyber-Physical Systems (CPS) are tight integrations of computational and physical worlds for various kinds of applications. For example, a humanoid robot, which is a typical application of CPS, has required timing constraints, low-latency execution, and parallel processing to achieve fine-grained real-time execution. Therefore low-latency parallel real-time computing is an important factor for CPS. In order to achieve such CPS applications, commercial off-the-shelf systems including processors and operating systems are difficult due to many requirements including such system performance and space constraints, and hence proprietary systems are favored. We had developed Dependable Responsive Multithreaded Processor I (D-RMTP I), which has one Responsive Multithreaded Processing Unit (RMT PU) with an 8-way prioritized Simultaneous Multithreading architecture, for parallel real-time computing. In addition, we have developed a high-end processor of D-RMTP I, called Dependable Responsive Multithreaded Processor II (D-RMTP II). D-RMTP II has two RMT PUs for high throughput and eight Flower cores for I/O processing. Our previous work presented Responsive Task, which is a low-latency real-time task with the interrupt wake-up structure to occupy a hardware thread in D-RMTP I for fine-grained real-time execution. Responsive Task can be executed in dozens of microsecond periods with low-jitter though executing real-time tasks simultaneously. Unfortunately, Responsive Task does not support parallel computing. This paper presents Parallel Responsive Task, which is an extension to Responsive Task for parallel computing on D-RMTP II. Evaluations show that Parallel Responsive Task improves the throughput and achieves fine-grained real-time execution with reasonable overhead.