This paper proposes an automatic attack construction algorithm in order to find potential attacks on security protocols. It is based on a dynamic strand space model,which enhances the original strand space model by introducing active nodes on strands so as to characterize the dynamic procedure of protocol execution. With exact causal dependency relations between messages considered in the model, this algorithm can avoid state space explosion caused by asynchronous composition. In order to get a finite state space, a new method called strand-added on demand is exploited, which extends a bundle in an incremental manner without requiring explicit configuration of protocol execution parameters. A finer granularity model of term structure is also introduced, in which subterms are divided into check subterms and data subterms. Moreover, data subterms can be further classified based on the compatible data subterm relation to obtain automatically the finite set of valid acceptable terms for an honest principal. In this algorithm, terms core is designed to represent the intruder’s knowledge compactly, and forward search technology is used to simulate attack patts easily. Using this algorithm, a new attack on the Dolve-Yao protocol can be found, which is even more harmful because the secret is revealed before the session terminates.