The fracture debonding failure of cement plug/casing interface caused by the migration of underground fluid with pressure accumulation imposed serious challenges to wellbore integrity of abandoned wells. This paper presents an investigation with a view of quantifying the relationships between the fracture debonding height and the migration time of underground fluid. A new 3D numerical model of cement plug/casing/cement sheath/formation system based on the cohesive zone method, which was validated by microannulus experiment, was developed to simulate the fracture debonding process. And then the relationships between fracture debonding height and propagation pressure was studied. Additionally, the influence of horizontal in-situ stress, cement plug mechanical parameters, and interface properties on the fracture debonding height and development geometry were also analyzed. The results of research indicated that the minimum horizontal in-situ stress played a decisive role in controlling the fracture propagation of cement/casing interface. Debonding fracture propagated along the whole circumference of the interface with the same height for the case that the horizontal in-situ stress was uniform, while propagated along a certain circumference angle of the interface with the maximum height in the direction of maximum horizontal principal stress for the case that the horizontal in-situ stress was non-uniform. The results of numerical analysis showed that lower elastic modulus and Poisson's ratio of cement plug, higher cement plug permeability, and larger critical normal strength and critical shear strength were beneficial to decrease the fracture debonding height and reduce the risk of debonding failure of the cement plug/casing interface. Finally, some effective measures to maintain the sealing integrity of abandoned wells were proposed.