Online testing is critical to ensuring reliable operations of the next generation of supercomputers based on a kilo-core network-on-chip (NoC) interconnection fabric. We present a parallel software-based self-testing (SBST) solution that makes use of the bounded model checking (BMC) technique to generate test sequences and parallel packets. In this method, the parallel SBST with BMC derives the leading sequence for each routers internal function and detects all functionally- testable faults related to the function. A Monte-Carlo simulation algorithm is then used to search for the approximately optimum configuration of the parallel packets, which guarantees the test quality and minimizes the test cost. Finally, a multi-threading technology is used to ensure that the Monte-Carlo simulation can reach the approximately optimum configuration in a large random space and reduce the generating time of the parallel test. Experimental results show that the proposed method achieves a high fault coverage with a reduced test overhead. Moreover, by performing online testing in the functional mode with SBST, it effectively avoids the over-testing problem caused by functionally untestable turns in kilo-core NoCs.