Finite control set model predictive torque control (FCS-MPTC) strategy has been widely used in induction motor (IM) control due to its fast response characteristic. Although the dynamics of the FCS-MPTC method are highly commended, its steady-state performance—ripple deserves attention in the meantime. To improve the steady-state performance of the IM drives, this paper proposes an improved FCS-MPTC strategy, based on a novel fuzzy adaptive speed controller and an adaptive weighting factor, tuning strategy to reduce the speed, torque and flux ripples caused by different factors. Firstly, a discrete predicting plant model (PPM) with a new flux observer is established, laying the ground for achieving an FCS-MPTC algorithm accurately. Secondly, after analyzing the essential factors in establishing a fuzzy adaptive PI controller, with high ripple suppression capacity, an improved three-dimensional controller is designed. Simultaneously, the implementation procedures of the fuzzy adaptive PI controller-based FCS-MPTC are presented. Considering that a weighting factor must be employed in the cost function of an FCS-MPTC method, system ripples increase if the value of the weighting factor is inappropriate. Then, on that basis, a novel fuzzy adaptive theory-based weighting factor tuning strategy is proposed, with the real-time torque and flux performance balanced. Finally, both simulation and hardware-in-loop (HIL) test are conducted on a 1.1 kW IM drive to verify the proposed ripple reduction algorithms.