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Decoy states have recently been proposed as a useful method for substantially improving the performance of quantum key distribution (QKD). Considering the Scarani-Acin-Ribordy-Gisin protocol (SARG04) with a heralded single photon source (HSPS), we review the general model of HSPS QKD system with a threshold detector, and analyze the SARG04 non-decoy-state protocol, SARG04 infinite active decoy-state protocol and SARG04 decoy-state protocol combining active decoy state method and passive decoy state method. Furthermore, we discuss the choice of optimal signal intensity for HSPS QKD with and without decoy states and obtain the condition that the optimal signal intensity satisfies. The simulation and analysis results show that the decoy state method can substantially improve the performance of SARG04 protocol with HSPS and the performance of SARG04 protocol with HSPS is better than that of BB84 protocol with HSPS. The decoy state method weakens the dependence of the optimal signal intensity on the overall transmission probability.