Modeling　the　implied　volatility　has　received　extensive　attention,　as　the　implied　volatility　is　an　important　parameter　in　option　pricing.　Usually　the　implied　volatility　can　be　approximated　by　fitting　a　polynomial　about　the　strike　and　the　maturity　or　by　stochastic　methods.　In　this　article,　a　Gaussian　semi-parametric　model　is　proposed　based　on　the　quadratic　polynomial　semi-parametric　model　suggested　by　Borovkova.　In　the　new　model,　the　Gaussian　function　is　used　to　construct　a　smooth　term　substituting　the　quadratic　term　in　the　polynomial　model,　and　the　arbitrage-free　constraints　are　used　to　calibrate　the　model.　The　empirical　tests　show　that　the　Gaussian　semi-parametric　model　has　a　better　performance　in　fitting　and　forecasting.　©　The　Author(s)　2017.