Stark-chirpedrapidadiabaticpassage(SCRAP)isanimportanttechniqueusedforcoherentquantumcontrols.Inthispaperweinvestigatehowthepractically-existingdissipationofthesysteminfluencesontheefficiencyofthepassage,andthusthefidelitiesoftheSCRAP-basedquantumgates.Withflux-biasedJosephsonqubitsasaspecificalexample,ourresultsshowclearlythattheefficiencyofthelogicgatesimplementedbySCRAParerobustagainsttheweakdissipation.Theinfluenceduetothenon-adiabtictransitionsbetweentheadiabaticpassagesiscomparativelysignificantlysmall.Therefore,theSCRAP-basedlogicgatesshouldbefeasiblefortherealisticphysicalsystemswithnoises.