Various parallel applications, such as numerical convergent computation and multimedia processing, have intrinsic tolerance to inaccuracies that allow soft errors, i.e. bit flips, on a chip. However, existing Network-on-Chips (NoCs) guarantee error-free data transfer; thus, encountering limits to reduce the power consumption. In this context, we propose an approximate dual-voltage NoC, called AxNoC. An AxNoC router uses a per-flit look-ahead power management so that headers and important-data flits are perfectly transferred at a high voltage while the remaining flits may incur bit flips by decreasing the supply voltage. An AxNoC router isolates the critical path when the supply voltage is low since such a critical path is enabled only at high voltage. The critical path isolation enables low-voltage operation to work at the same operating frequency at high voltage. An AxNoC router was implemented using a 28nm process and the evaluation results illustrate its efficiency to reduce the power consumption reaching up to 43% while incurring a small area overhead that does not exceed 6.2%. We also demonstrate that AxNoC exhibits an acceptable accuracy illustrated in a sufficiently small geomean of error.