This paper utilizes an effective control strategy to suppress the regenerative chatter in a plunge-grinding process. To begin with, the dynamical interaction between the workpiece and the grinding wheel is considered as a major factor influencing the grinding stability. Mathematically, the grinding stability is studied through numerical eigenvalue analysis. Consequently, critical chatter boundaries are obtained to distinguish the chatter-free and the chatter regions. As known, the grinding is unstable and the chatter happens in the chatter region. To observe the chatter vibrations, an analytical method and numerical simulations are employed. As a result, chatter vibrations both with and without losing contact between the workpiece and the wheel are obtained. Meanwhile, the coexistence of the chatter and the stable grinding is also found in the chatter-free region. Finally, a control strategy involving spindle speed variation (SSV) is introduced to suppress the chatter. Then, its effectiveness is analytically investigated in terms of the method of multiple scales (MMS).