In　this　paper,　we　consider　the　numerical　approximations　for　the　commonly　used　binary　fluid-surfactant　phase　field　model　that　consists　two　nonlinearly　coupled　Cahn-Hilliard　equations.　The　main　challenge　in　solving　the　system　numerically　is　how　to　develop　easy-to-implement　time　stepping　schemes　while　preserving　the　unconditional　energy　stability.　We　solve　this　issue　by　developing　two　linear　and　decoupled,　first　order　and　a　second　order　time-stepping　schemes　using　the　so-called　＂invariant　energy　quadratization＂　approach　for　the　double　well　potentials　and　a　subtle　explicit-implicit　technique　for　the　nonlinear　coupling　potential.　Moreover,　the　resulting　linear　system　is　well-posed　and　the　linear　operator　is　symmetric　positive　definite.　We　rigorously　prove　the　first　order　scheme　is　unconditionally　energy　stable.　Various　numerical　simulations　are　presented　to　demonstrate　the　stability　and　the　accuracy　thereafter.