Synchronous condenser is an important equipment to provide reactive power compensation and voltage support in the ultra-high voltage direct current (UHVDC) transmission system. The safety and reliability of its operation are of great significance to UHVDC projects. A fault diagnosis method based on stator branch circulating current to address the challenges of diagnosing minor stator inter-turn short-circuits (SISC) and locating fault slots is proposed in this paper. Firstly, from the perspective of a single coil in the stator branch, the influence of different positions of SISC faults on the armature magnetomotive force and stator branch circulating current is analyzed. Secondly, a field-circuit coupling model for SISC in synchronous condenser is established to simulate the fault characteristics at different positions. Finally, the variation law of the stator branch circulating current is summarized at different positions. The results of simulation and experiment show that when the number of turns of SISC stays the same, the closer the short circuit position is to the axis of the branch winding, the larger the amplitude of the stator circulating current, the further the short circuit position is from the winding axis, the smaller the amplitude of the stator branch circulating current.