High　cost　of　training　time　caused　by　multi-step　adversarial　example　generation　is　a　major　challenge　in　adversarial　training.　Previous　methods　try　to　reduce　the　computational　burden　of　adversarial　training　using　single-step　adversarial　example　generation　schemes,　which　can　effectively　improve　the　efficiency　but　also　introduce　the　problem　of　＇catastrophic　overfitting＇,　where　the　robust　accuracy　against　Fast　Gradient　Sign　Method　(FGSM)　can　achieve　nearby　100%　whereas　the　robust　accuracy　against　Projected　Gradient　Descent　(PGD)　suddenly　drops　to　0%　over　a　single　epoch.　To　address　this　issue,　we　focus　on　single-step　adversarial　training　scheme　in　this　paper　and　propose　a　novel　Fast　Gradient　Sign　Method　with　PGD　Regularization　(FGSMPR)　to　boost　the　efficiency　of　adversarial　training　without　catastrophic　overfitting.　Our　core　observation　is　that　single-step　adversarial　training　can　not　simultaneously　learn　robust　internal　representations　of　FGSM　and　PGD　adversarial　examples.　Therefore,　we　design　a　PGD　regularization　term　to　encourage　similar　embeddings　of　FGSM　and　PGD　adversarial　examples.　The　experiments　demonstrate　that　our　proposed　method　can　train　a　robust　deep　network　for　L∞　-perturbations　with　FGSM　adversarial　training　and　reduce　the　gap　to　multi-step　adversarial　training.　©　2021,　Springer　Nature　Switzerland　AG.