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Purpose: Semi-active control is considered to be very interesting for its engineering sophistication/effectiveness like the active control strategy, however, requiring significantly lesser amount of control effort/input. In view of the devastating damages of soft-storey building structures in case of real-life seismic events, a study on semi-active vibration control for vulnerable structures like soft-storey buildings appears very interesting. Methods: The magnetorheological (MR) damper is taken as the control device which produces control force through modulating its damping coefficient with the help of external input voltages in a semi-active control framework based on the widely used Linear Quadratic Gaussian (LQG) control. The Bouc–Wen hysteresis model is considered to calculate the control force. A realistic five-storey building with soft-storey at the ground is considered for validation. Besides, the performance of LQG control is compared with the proportional-integral-derivative (PID) control. Results: It is observed that LQG-based semi-active control strategy has been able to perform satisfactorily (in reducing soft-storey response) with the cost of surprisingly insignificant amount of control effort (with supply voltage in the range, 0–2.5 V) by reducing the peak response as 67.5%, 78.05%, 67.57%, 75%, and 51.02% against El Centro, Northridge, Kobe, Bhuj, and Tohoku earthquakes, respectively, while 68.85%, 79.42%, 65.26%, 73.38%, and 51.65% in case of root-mean-square response. Higher range of supply voltage is found to provide even better control performance. Conclusion: In view of the satisfactory control performance, the semi-active control with MR dampers using LQG control is well encouraging in protecting the highly vulnerable soft-storey building structures under seismic events. [ABSTRACT FROM AUTHOR]