The inter-turn short circuits fault of field windings is a common fault in generators. According to the multi-loop method of AC machines, this paper proposes multi-loop mathematical model of turbine generator with inter-turn short circuits fault of field windings. Based on the model, the normal operation and the short circuits fault operation of generator with no load have been simulated combining with the actual structure of a 300MW turbine generator. The time-varying mutual inductances between stator and rotor winding are calculated, from simulation results, the field current and stator voltages show the model reasonable under normal operation, After the field windings short faults, the field current increases gradually to a new constant value under the constant field voltage, the transient feature of stator voltage are obtained, which provides the basis for further fault analysis and fault diagnosis of turbine generator with field winding inter-turn short circuits.