Underwaterrobotisanewresearchfieldwhichisemergingquicklyinrecentyears.PreviousresearchesinthisfieldfocusonRemotelyOperatedVehicles(ROVs),AutonomousUnderwaterVehicles(AUVs),underwatermanipulators,etc.Fishrobot,whichisanewtypeofunderwaterbiomimeticrobot,hasattractedgreatattentionbecauseofitssilenceinmovingandenergyefficiencycomparedtoconventionalpropeller-orientedpropulsivemechanism.However,mostofresearchesonfishrobotshavebeencarriedoutviaempiricalorexperimentalapproaches,notbasedondynamicoptimality.Inthispaper,weproposedananalyticaloptimizationapproachwhichcanguaranteethemaximumpropulsivevelocityoffishrobotinthegivenparametricconditions.First,adynamicmodelof3-joint(4links)carangiformfishrobotisderived,usingwhichtheinfluencesofparametersofinputtorquefunctions,suchasamplitude,frequencyandphasedifference,onitsvelocityareinvestigatedbysimulation.Second,themaximumvelocityofthefishrobotisoptimizedbycombiningGeneticAlgorithm(GA)andHillClimbingAlgorithm(HCA).GAisusedtogeneratetheinitialoptimalparametersoftheinputfunctionsofthesystem.Then,theparametersareoptimizedagainbyHCAtoensurethatthefinalsetofparametersisthe"near"globaloptimization.Finally,bothsimulationsandprimitiveexperimentsarecarriedouttoprovethefeasibilityoftheproposedmethod.