An H-bridge inverter with LC (inductor-capacitor) filter output allows the conversion of DC (direct current) power to AC (alternating current) power that has been used in a variety of applications, such as uninterruptible power supplies, AC motor drives, and renewable energy source systems. The fast finite-time sliding mode control (FFTSMC) features acceleration of the system state towards the equilibrium position as well as conserving insensitivity against internal parameter fluctuations as well as external load disturbances falling within the predetermined bounds. However, the FFTSMC would potentially witness chattering or steady-state errors as indefinite margins come to be exaggerated or underestimated. The chattering in the sliding mode control practice is oscillatory defective behavior. It induces inefficient operation, higher switching power losses in the transistor circuits, as well as saturated actuators, thus impairing the inverter’s output energy efficiency and raising harmonic distortion. Therefore, this paper presents the H-bridge inverter with LC filter output, which is controlled by a grey prediction fast finite-time sliding mode trajectory tracking. A more highly accurate grey prediction model based on the centered approximation methodology is deployed to vanish the chattering as well as steady-state errors. Taking into account the union of grey prediction and FFTSMC, a feedback-controlled H-bridge inverter with LC filter output allows attaining a highly efficient as well as quality sine-wave output voltage. The presented state-feedback control strategy is robust, less complex, attains more rapid convergence, and is highly accurate. The design process, computer simulation, as well as experimental results of the proposed state-feedback control strategy established that the H-bridge inverter with LC filter output has the capability to exhibit fast dynamic response time as well as good steady-state tracking behavior of the output voltage under step-loading changes and nonlinear loading conditions.