With aggressive technology scaling in deep submicron era, burgeoning transistors make chips more susceptible to failures. It is inevitable that process variation is gradually becoming a crucial challenge in the IC design. In addition, aging leads to faults, shortening the lifetime of the circuits. Networks-on-chip also come to the problems caused by variations and aging, leading to degraded performance and erroneous behaviors. Faults may occur in numerous locations of the on-chip networks and once they occur in the control path, more severe effects such as deadlock and livelock are expected. In this paper, we present a fine-grained mechanism to tolerate faults in the routing computation units without disabling the faulty routers. By applying this mechanism, routing and packet-receiving services are separated. The faulty routing computation unit is replaced by a light-weight redundant circuit, providing static but reliable routing services. The other components in this router are still functional retaining the on-chip performance. Experimental results indicate that the on-chip network with the proposed mechanism is fault-tolerant when 14% of all routing computation modules are suffering from faults. The area overhead and power consumption of the proposed method is around 7.29% and 6.20% over the baseline approach.