As process technology is scaled down, a typical system on a chip (SoC) becomes denser. In scaled process technology, process variation becomes greater and increasingly affects the SoC circuits. Moreover, the process variation strongly affects network-on-chips (NoCs) that have a synchronous network across the chip. Therefore, its network frequency is degraded. We propose a process-variation-adaptive NoC with a variation-adaptive variable-cycle router (VAVCR). The proposed VAVCR can configure its cycle latency adaptively on a processor core basis, corresponding to the process variation. It can increase the network frequency, which is limited by the process variation in a conventional router. Furthermore, we propose a variable-cycle pipeline adaptive routing (VCPAR) method with VAVCR; the proposed VCPAR can reduce packet latency and has tolerance to network congestion. The total execution time reduction of the proposed VAVCR with VCPAR is 15.7%, on average, for five task graphs.