We　propose　a　protocol　for　complete　Bell-state　analysis　for　two　superconducting-quantum-interference-device　qubits.　The　Bell-state　analysis　could　be　completed　by　using　a　sequence　of　microwave　pulses　designed　by　the　transitionless　tracking　algorithm,　which　is　a　useful　method　in　the　technique　of　shortcut　to　adiabaticity.　After　the　whole　process,　the　information　for　distinguishing　four　Bell　states　will　be　encoded　on　two　auxiliary　qubits,　while　the　Bell　states　remain　unchanged.　One　can　read　out　the　information　by　detecting　the　auxiliary　qubits.　Thus　the　Bell-state　analysis　is　nondestructive.　The　numerical　simulations　show　that　the　protocol　possesses　a　high　success　probability　of　distinguishing　each　Bell　state　with　current　experimental　technology　even　when　decoherence　is　taken　into　account.　Thus,　the　protocol　may　have　potential　applications　for　the　information　readout　in　quantum　communications　and　quantum　computations　in　superconducting　quantum　networks.