In this paper, we present an authentication scheme to prevent impersonation attack in link state routing protocol. The existing authentication schemes are either simple to compute but vulnerable to attacks of too robust against attacks but has exponential computation cost. We introduce a double authentication (DA) scheme which provides authentication to the routing information data carried by link state routing packets. In this scheme every router needs to sign the routing data twice with two different keys using a group keying scheme, which is based on one-way hash function. Based on our performance assessment, we found that this scheme is simpler to implement, computationally efficient and provides the degree of robustness desired with less communication overhead but has higher memory requirement.