Routing table size and routing path length are two critical measures for evaluating a routing algorithm, and there exists a tradeoff problem between them. Compact routing refers to the design of routing algorithms obtaining relatively optimal tradeoffs between the above two measures. So far, researchers have proposed quite a few universal compact routing schemes, which have high optimized bounds on routing table size and path length for arbitrary network topologies. However, as real-world networks usually have specific topologies, the universal schemes are possibly sub-optimal on them for not exploiting the topological properties. Recent work discovered many real-world networks had scale-free topologies. By exploiting the power-law and strong clustering features, a compact routing scheme with additive stretch for this class of networks is presented in this paper. By separating a network into a backbone tree and shortcuts, this scheme ensures between any source node and destination node in a network, the routing path length is at most an additive factor of b longer than the shortest path between them, and the local routing table at each node is upper bounded by O(clog2n) bits, wherein b and c are parameters related to the network topology. Experimental results show that b and c have small values in scale-free networks, and the proposed scheme can achieve better average-case performance than known schemes.