This paper presents an linear quadratic Gaussian (LQG)-based robust control strategy for active noise reduction in a 3D enclosure wherein acoustic-structure interaction dynamics is present. The acoustic disturbance is created by the piezo-actuated vibrating boundary surface of the enclosure. The control signal is generated by the speaker which is noncollocated with the sensing microphone mounted inside the enclosure. The dynamic model of the system is obtained using frequency-domain system identification techniques. The state weighting matrix in the LQG cost function is determined analytically in the closed-form which allows the control designer to directly penalize the total acoustic energy of the system. The robustness of the controller is also ensured to guarantee the closed-loop stability against the unmodeled dynamics and parametric uncertainties. Simulation and experiment results are given which demonstrate the effectiveness of the proposed control methodology.