Numerical simulations and analyses have been applied to find the relationships between magnetic flux,ring current,free energy of superconducting rings and external magnetic field.It is found that a double-junction superconducting ring has a different behavior from a single-junction ring.When the Ic values are identical,a double-junction ring has a non-hysteresis behavior when β＜2.The hysteresis exists only when β≥2.And a double-junction ring has a double-branch solution with 2Φ0 period.