The stability of high-temperature superconducting current leads for cryogenic devices are investigated. By assuming full transition from superconducting state to normal state at a transition temperature, the HTS current at a transition temperature, the HTS current lead shows bifurcation phenomenon. There is a bifurcation shape-factor, HTS leads have three steady state. Below the bifurcation shape-factor, the superconducting current lead is unconditionally stable, because there exists only one steady-factor HTS current lead is conditionally stable depending on the shape and intensity of disturbance.