In　this　work,　we　propose　a　composite　pulses　(CPs)　scheme　by　modulating　phases　to　achieve　high　fidelity　population　transfer　in　three-level　systems.　To　circumvent　the　obstacle　that　not　enough　variables　are　exploited　to　eliminate　the　systematic　errors　in　the　transition　probability,　we　put　forward　a　cost　function　to　find　the　optimal　value.　The　cost　function　is　independently　constructed　either　in　ensuring　an　accurate　population　of　the　target　state,　or　in　suppressing　the　population　of　the　leakage　state,　or　both　of　them.　The　results　demonstrate　that　population　transfer　is　implemented　with　high　fidelity　even　when　existing　the　deviations　in　the　coupling　coefficients.　Furthermore,　our　CPs　scheme　can　be　extensible　to　arbitrarily　long　pulse　sequences.　As　an　example,　we　employ　the　CPs　sequence　for　achieving　the　three-atom　singlet　state　in　an　atom-cavity　system　with　ultrahigh　fidelity.　The　final　singlet　state　shows　robustness　against　deviations　and　is　not　seriously　affected　by　waveform　distortions.　Also,　the　singlet　state　maintains　a　high　fidelity　under　the　decoherence　environment.　©　2022　The　Author(s).　Published　by　IOP　Publishing　Ltd　on　behalf　of　the　Institute　of　Physics　and　Deutsche　Physikalische　Gesellschaft.