Four-switch three-phase inverter (FSTPI) is widely used as a cost-effective fault-tolerant topology of six-switch three-phase inverter with an open-phase fault. To solve the inherent dc-link capacitor voltage offset (CVO) issue of FSTPI, two dc-link capacitor voltage sensors are required in conventional model predictive torque control (MPTC) strategies. To improve the reliability and reduce the cost of induction motor (IM) drives, a modulated MPTC (M-MPTC) for FSTPI-fed IM with single dc-link voltage sensor is proposed in this article. Therein, the relationship of the CVO and the load current is established to obtain the fundamental component of CVO. The two capacitor voltages are reconstructed by single dc-link voltage sensor and the fundamental component of CVO. To suppress the CVO, a cost function that only contains the output voltage vector is designed. The inner relationship between the proposed M-MPTC with single dc-link voltage sensor and the conventional M-MPTC with two dc-link voltage sensors is derived. To retain the load current within the allowed range, a current constraint scheme is proposed and integrated into the M-MPTC. Various simulation and experimental studies are carried out to verify the effectiveness of the proposed strategy.